Daily Papers

We present Buffer Anytime, a framework for estimation of depth and normal maps (which we call geometric buffers) from video that eliminates the need for paired video--depth and video--normal training data. Instead of relying on large-scale annotated video datasets, we demonstrate high-quality video buffer estimation by leveraging single-image priors with temporal consistency constraints. Our zero-shot training strategy combines state-of-the-art image estimation models based on optical flow smoothness through a hybrid loss function, implemented via a lightweight temporal attention architecture. Applied to leading image models like Depth Anything V2 and Marigold-E2E-FT, our approach significantly improves temporal consistency while maintaining accuracy. Experiments show that our method not only outperforms image-based approaches but also achieves results comparable to state-of-the-art video models trained on large-scale paired video datasets, despite using no such paired video data.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

We introduce PyTorch Geometric, a library for deep learning on irregularly structured input data such as graphs, point clouds and manifolds, built upon PyTorch. In addition to general graph data structures and processing methods, it contains a variety of recently published methods from the domains of relational learning and 3D data processing. PyTorch Geometric achieves high data throughput by leveraging sparse GPU acceleration, by providing dedicated CUDA kernels and by introducing efficient mini-batch handling for input examples of different size. In this work, we present the library in detail and perform a comprehensive comparative study of the implemented methods in homogeneous evaluation scenarios.

Following the advent of NeRFs, 3D Gaussian Splatting (3D-GS) has paved the way to real-time neural rendering overcoming the computational burden of volumetric methods. Following the pioneering work of 3D-GS, several methods have attempted to achieve compressible and high-fidelity performance alternatives. However, by employing a geometry-agnostic optimization scheme, these methods neglect the inherent 3D structure of the scene, thereby restricting the expressivity and the quality of the representation, resulting in various floating points and artifacts. In this work, we propose a structure-aware Gaussian Splatting method (SAGS) that implicitly encodes the geometry of the scene, which reflects to state-of-the-art rendering performance and reduced storage requirements on benchmark novel-view synthesis datasets. SAGS is founded on a local-global graph representation that facilitates the learning of complex scenes and enforces meaningful point displacements that preserve the scene's geometry. Additionally, we introduce a lightweight version of SAGS, using a simple yet effective mid-point interpolation scheme, which showcases a compact representation of the scene with up to 24times size reduction without the reliance on any compression strategies. Extensive experiments across multiple benchmark datasets demonstrate the superiority of SAGS compared to state-of-the-art 3D-GS methods under both rendering quality and model size. Besides, we demonstrate that our structure-aware method can effectively mitigate floating artifacts and irregular distortions of previous methods while obtaining precise depth maps. Project page https://eververas.github.io/SAGS/.

We present GI-GS, a novel inverse rendering framework that leverages 3D Gaussian Splatting (3DGS) and deferred shading to achieve photo-realistic novel view synthesis and relighting. In inverse rendering, accurately modeling the shading processes of objects is essential for achieving high-fidelity results. Therefore, it is critical to incorporate global illumination to account for indirect lighting that reaches an object after multiple bounces across the scene. Previous 3DGS-based methods have attempted to model indirect lighting by characterizing indirect illumination as learnable lighting volumes or additional attributes of each Gaussian, while using baked occlusion to represent shadow effects. These methods, however, fail to accurately model the complex physical interactions between light and objects, making it impossible to construct realistic indirect illumination during relighting. To address this limitation, we propose to calculate indirect lighting using efficient path tracing with deferred shading. In our framework, we first render a G-buffer to capture the detailed geometry and material properties of the scene. Then, we perform physically-based rendering (PBR) only for direct lighting. With the G-buffer and previous rendering results, the indirect lighting can be calculated through a lightweight path tracing. Our method effectively models indirect lighting under any given lighting conditions, thereby achieving better novel view synthesis and relighting. Quantitative and qualitative results show that our GI-GS outperforms existing baselines in both rendering quality and efficiency.

Recently, significant advances have been made in 3D object generation. Building upon the generated geometry, current pipelines typically employ image diffusion models to generate multi-view RGB images, followed by UV texture reconstruction through texture baking. While 3D geometry generation has improved significantly, supported by multiple open-source frameworks, 3D texture generation remains underexplored. In this work, we systematically investigate 3D texture generation through the lens of three core dimensions: reference-texture alignment, geometry-texture consistency, and local texture quality. To tackle these issues, we propose MVPainter, which employs data filtering and augmentation strategies to enhance texture fidelity and detail, and introduces ControlNet-based geometric conditioning to improve texture-geometry alignment. Furthermore, we extract physically-based rendering (PBR) attributes from the generated views to produce PBR meshes suitable for real-world rendering applications. MVPainter achieves state-of-the-art results across all three dimensions, as demonstrated by human-aligned evaluations. To facilitate further research and reproducibility, we also release our full pipeline as an open-source system, including data construction, model architecture, and evaluation tools.

The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in Euclidean space, such as biomolecules, materials, and other physical systems. In this work, we propose a geometric version of the WL test (GWL) for discriminating geometric graphs while respecting the underlying physical symmetries: permutations, rotation, reflection, and translation. We use GWL to characterise the expressive power of geometric GNNs that are invariant or equivariant to physical symmetries in terms of distinguishing geometric graphs. GWL unpacks how key design choices influence geometric GNN expressivity: (1) Invariant layers have limited expressivity as they cannot distinguish one-hop identical geometric graphs; (2) Equivariant layers distinguish a larger class of graphs by propagating geometric information beyond local neighbourhoods; (3) Higher order tensors and scalarisation enable maximally powerful geometric GNNs; and (4) GWL's discrimination-based perspective is equivalent to universal approximation. Synthetic experiments supplementing our results are available at https://github.com/chaitjo/geometric-gnn-dojo

Structural and Positional Encodings can significantly improve the performance of Graph Neural Networks in downstream tasks. Recent literature has begun to systematically investigate differences in the structural properties that these approaches encode, as well as performance trade-offs between them. However, the question of which structural properties yield the most effective encoding remains open. In this paper, we investigate this question from a geometric perspective. We propose a novel structural encoding based on discrete Ricci curvature (Local Curvature Profiles, short LCP) and show that it significantly outperforms existing encoding approaches. We further show that combining local structural encodings, such as LCP, with global positional encodings improves downstream performance, suggesting that they capture complementary geometric information. Finally, we compare different encoding types with (curvature-based) rewiring techniques. Rewiring has recently received a surge of interest due to its ability to improve the performance of Graph Neural Networks by mitigating over-smoothing and over-squashing effects. Our results suggest that utilizing curvature information for structural encodings delivers significantly larger performance increases than rewiring.

The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric boundaries. Triangularized geometric boundaries are well understood and ubiquitous in engineering applications. However, it is notoriously difficult to integrate them into machine learning approaches due to their heterogeneity with respect to size and orientation. In this work, we introduce an effective theory to model particle-boundary interactions, which leads to our new Boundary Graph Neural Networks (BGNNs) that dynamically modify graph structures to obey boundary conditions. The new BGNNs are tested on complex 3D granular flow processes of hoppers, rotating drums and mixers, which are all standard components of modern industrial machinery but still have complicated geometry. BGNNs are evaluated in terms of computational efficiency as well as prediction accuracy of particle flows and mixing entropies. BGNNs are able to accurately reproduce 3D granular flows within simulation uncertainties over hundreds of thousands of simulation timesteps. Most notably, in our experiments, particles stay within the geometric objects without using handcrafted conditions or restrictions.

Problems involving geometric data arise in a variety of fields, including computer vision, robotics, chemistry, and physics. Such data can take numerous forms, such as points, direction vectors, planes, or transformations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric algebra, which offers an efficient 16-dimensional vector space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a transformer, GATr is scalable, expressive, and versatile. In experiments with n-body modeling and robotic planning, GATr shows strong improvements over non-geometric baselines.

In this paper, we present Gaussian Splatting based text-to-3D generation (GSGEN), a novel approach for generating high-quality 3D objects. Previous methods suffer from inaccurate geometry and limited fidelity due to the absence of 3D prior and proper representation. We leverage 3D Gaussian Splatting, a recent state-of-the-art representation, to address existing shortcomings by exploiting the explicit nature that enables the incorporation of 3D prior. Specifically, our method adopts a progressive optimization strategy, which includes a geometry optimization stage and an appearance refinement stage. In geometry optimization, a coarse representation is established under a 3D geometry prior along with the ordinary 2D SDS loss, ensuring a sensible and 3D-consistent rough shape. Subsequently, the obtained Gaussians undergo an iterative refinement to enrich details. In this stage, we increase the number of Gaussians by compactness-based densification to enhance continuity and improve fidelity. With these designs, our approach can generate 3D content with delicate details and more accurate geometry. Extensive evaluations demonstrate the effectiveness of our method, especially for capturing high-frequency components. Video results are provided at https://gsgen3d.github.io. Our code is available at https://github.com/gsgen3d/gsgen

Recovering high-quality depth maps from compressed sources has gained significant attention due to the limitations of consumer-grade depth cameras and the bandwidth restrictions during data transmission. However, current methods still suffer from two challenges. First, bit-depth compression produces a uniform depth representation in regions with subtle variations, hindering the recovery of detailed information. Second, densely distributed random noise reduces the accuracy of estimating the global geometric structure of the scene. To address these challenges, we propose a novel framework, termed geometry-decoupled network (GDNet), for compressed depth map super-resolution that decouples the high-quality depth map reconstruction process by handling global and detailed geometric features separately. To be specific, we propose the fine geometry detail encoder (FGDE), which is designed to aggregate fine geometry details in high-resolution low-level image features while simultaneously enriching them with complementary information from low-resolution context-level image features. In addition, we develop the global geometry encoder (GGE) that aims at suppressing noise and extracting global geometric information effectively via constructing compact feature representation in a low-rank space. We conduct experiments on multiple benchmark datasets, demonstrating that our GDNet significantly outperforms current methods in terms of geometric consistency and detail recovery. In the ECCV 2024 AIM Compressed Depth Upsampling Challenge, our solution won the 1st place award. Our codes are available at: https://github.com/Ian0926/GDNet.

Advanced generative model (e.g., diffusion model) derived from simplified continuity assumptions of data distribution, though showing promising progress, has been difficult to apply directly to geometry generation applications due to the multi-modality and noise-sensitive nature of molecule geometry. This work introduces Geometric Bayesian Flow Networks (GeoBFN), which naturally fits molecule geometry by modeling diverse modalities in the differentiable parameter space of distributions. GeoBFN maintains the SE-(3) invariant density modeling property by incorporating equivariant inter-dependency modeling on parameters of distributions and unifying the probabilistic modeling of different modalities. Through optimized training and sampling techniques, we demonstrate that GeoBFN achieves state-of-the-art performance on multiple 3D molecule generation benchmarks in terms of generation quality (90.87% molecule stability in QM9 and 85.6% atom stability in GEOM-DRUG. GeoBFN can also conduct sampling with any number of steps to reach an optimal trade-off between efficiency and quality (e.g., 20-times speedup without sacrificing performance).

3D Gaussian splatting (3DGS) has recently emerged as an alternative representation that leverages a 3D Gaussian-based representation and introduces an approximated volumetric rendering, achieving very fast rendering speed and promising image quality. Furthermore, subsequent studies have successfully extended 3DGS to dynamic 3D scenes, demonstrating its wide range of applications. However, a significant drawback arises as 3DGS and its following methods entail a substantial number of Gaussians to maintain the high fidelity of the rendered images, which requires a large amount of memory and storage. To address this critical issue, we place a specific emphasis on two key objectives: reducing the number of Gaussian points without sacrificing performance and compressing the Gaussian attributes, such as view-dependent color and covariance. To this end, we propose a learnable mask strategy that significantly reduces the number of Gaussians while preserving high performance. In addition, we propose a compact but effective representation of view-dependent color by employing a grid-based neural field rather than relying on spherical harmonics. Finally, we learn codebooks to compactly represent the geometric and temporal attributes by residual vector quantization. With model compression techniques such as quantization and entropy coding, we consistently show over 25x reduced storage and enhanced rendering speed compared to 3DGS for static scenes, while maintaining the quality of the scene representation. For dynamic scenes, our approach achieves more than 12x storage efficiency and retains a high-quality reconstruction compared to the existing state-of-the-art methods. Our work provides a comprehensive framework for 3D scene representation, achieving high performance, fast training, compactness, and real-time rendering. Our project page is available at https://maincold2.github.io/c3dgs/.

We aim to address a significant but understudied problem in the anime industry, namely the inbetweening of cartoon line drawings. Inbetweening involves generating intermediate frames between two black-and-white line drawings and is a time-consuming and expensive process that can benefit from automation. However, existing frame interpolation methods that rely on matching and warping whole raster images are unsuitable for line inbetweening and often produce blurring artifacts that damage the intricate line structures. To preserve the precision and detail of the line drawings, we propose a new approach, AnimeInbet, which geometrizes raster line drawings into graphs of endpoints and reframes the inbetweening task as a graph fusion problem with vertex repositioning. Our method can effectively capture the sparsity and unique structure of line drawings while preserving the details during inbetweening. This is made possible via our novel modules, i.e., vertex geometric embedding, a vertex correspondence Transformer, an effective mechanism for vertex repositioning and a visibility predictor. To train our method, we introduce MixamoLine240, a new dataset of line drawings with ground truth vectorization and matching labels. Our experiments demonstrate that AnimeInbet synthesizes high-quality, clean, and complete intermediate line drawings, outperforming existing methods quantitatively and qualitatively, especially in cases with large motions. Data and code are available at https://github.com/lisiyao21/AnimeInbet.

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as geometric graphs, i.e., graphs with nodes positioned in the Euclidean space given an arbitrarily chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as Galilean invariance. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume. Notably, our representation does not rely on a regular grid, is supervised directly by the target surface alone, and also handles open surfaces with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids and show that our method surpasses recent state-of-the-art techniques in terms of both surface and edge-based metrics.

Automatic math problem solving has recently attracted increasing attention as a long-standing AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams, and theorem knowledge. However, the existing methods were highly dependent on handcraft rules and were merely evaluated on small-scale datasets. Therefore, we propose a Geometric Question Answering dataset GeoQA, containing 4,998 geometric problems with corresponding annotated programs, which illustrate the solving process of the given problems. Compared with another publicly available dataset GeoS, GeoQA is 25 times larger, in which the program annotations can provide a practical testbed for future research on explicit and explainable numerical reasoning. Moreover, we introduce a Neural Geometric Solver (NGS) to address geometric problems by comprehensively parsing multimodal information and generating interpretable programs. We further add multiple self-supervised auxiliary tasks on NGS to enhance cross-modal semantic representation. Extensive experiments on GeoQA validate the effectiveness of our proposed NGS and auxiliary tasks. However, the results are still significantly lower than human performance, which leaves large room for future research. Our benchmark and code are released at https://github.com/chen-judge/GeoQA .

We introduce Clifford Group Equivariant Simplicial Message Passing Networks, a method for steerable E(n)-equivariant message passing on simplicial complexes. Our method integrates the expressivity of Clifford group-equivariant layers with simplicial message passing, which is topologically more intricate than regular graph message passing. Clifford algebras include higher-order objects such as bivectors and trivectors, which express geometric features (e.g., areas, volumes) derived from vectors. Using this knowledge, we represent simplex features through geometric products of their vertices. To achieve efficient simplicial message passing, we share the parameters of the message network across different dimensions. Additionally, we restrict the final message to an aggregation of the incoming messages from different dimensions, leading to what we term shared simplicial message passing. Experimental results show that our method is able to outperform both equivariant and simplicial graph neural networks on a variety of geometric tasks.

Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing. We overcome these challenges by employing a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition without supervision. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights. BSP-Net directly outputs polygonal meshes from the inferred convexes. The generated meshes are watertight, compact (i.e., low-poly), and well suited to represent sharp geometry. We show that the reconstruction quality by BSP-Net is competitive with those from state-of-the-art methods while using much fewer primitives. We also explore variations to BSP-Net including using a more generic decoder for reconstruction, more general primitives than planes, as well as training a generative model with variational auto-encoders. Code is available at https://github.com/czq142857/BSP-NET-original.

3D Gaussian Splatting (3DGS) integrates the strengths of primitive-based representations and volumetric rendering techniques, enabling real-time, high-quality rendering. However, 3DGS models typically overfit to single-scene training and are highly sensitive to the initialization of Gaussian ellipsoids, heuristically derived from Structure from Motion (SfM) point clouds, which limits both generalization and practicality. To address these limitations, we propose GS-Net, a generalizable, plug-and-play 3DGS module that densifies Gaussian ellipsoids from sparse SfM point clouds, enhancing geometric structure representation. To the best of our knowledge, GS-Net is the first plug-and-play 3DGS module with cross-scene generalization capabilities. Additionally, we introduce the CARLA-NVS dataset, which incorporates additional camera viewpoints to thoroughly evaluate reconstruction and rendering quality. Extensive experiments demonstrate that applying GS-Net to 3DGS yields a PSNR improvement of 2.08 dB for conventional viewpoints and 1.86 dB for novel viewpoints, confirming the method's effectiveness and robustness.

Recently, methods leveraging diffusion model priors to assist monocular geometric estimation (e.g., depth and normal) have gained significant attention due to their strong generalization ability. However, most existing works focus on estimating geometric properties within the camera coordinate system of individual video frames, neglecting the inherent ability of diffusion models to determine inter-frame correspondence. In this work, we demonstrate that, through appropriate design and fine-tuning, the intrinsic consistency of video generation models can be effectively harnessed for consistent geometric estimation. Specifically, we 1) select geometric attributes in the global coordinate system that share the same correspondence with video frames as the prediction targets, 2) introduce a novel and efficient conditioning method by reusing positional encodings, and 3) enhance performance through joint training on multiple geometric attributes that share the same correspondence. Our results achieve superior performance in predicting global geometric attributes in videos and can be directly applied to reconstruction tasks. Even when trained solely on static video data, our approach exhibits the potential to generalize to dynamic video scenes.

3D Gaussian Splatting (3DGS) achieves fast and high-quality renderings by using numerous small Gaussians, which leads to significant memory consumption. This reliance on a large number of Gaussians restricts the application of 3DGS-based models on low-cost devices due to memory limitations. However, simply reducing the number of Gaussians to accommodate devices with less memory capacity leads to inferior quality compared to the quality that can be achieved on high-end hardware. To address this lack of scalability, we propose integrating a Flexible Level of Detail (FLoD) to 3DGS, to allow a scene to be rendered at varying levels of detail according to hardware capabilities. While existing 3DGSs with LoD focus on detailed reconstruction, our method provides reconstructions using a small number of Gaussians for reduced memory requirements, and a larger number of Gaussians for greater detail. Experiments demonstrate our various rendering options with tradeoffs between rendering quality and memory usage, thereby allowing real-time rendering across different memory constraints. Furthermore, we show that our method generalizes to different 3DGS frameworks, indicating its potential for integration into future state-of-the-art developments. Project page: https://3dgs-flod.github.io/flod.github.io/

We introduce RealmDreamer, a technique for generation of general forward-facing 3D scenes from text descriptions. Our technique optimizes a 3D Gaussian Splatting representation to match complex text prompts. We initialize these splats by utilizing the state-of-the-art text-to-image generators, lifting their samples into 3D, and computing the occlusion volume. We then optimize this representation across multiple views as a 3D inpainting task with image-conditional diffusion models. To learn correct geometric structure, we incorporate a depth diffusion model by conditioning on the samples from the inpainting model, giving rich geometric structure. Finally, we finetune the model using sharpened samples from image generators. Notably, our technique does not require video or multi-view data and can synthesize a variety of high-quality 3D scenes in different styles, consisting of multiple objects. Its generality additionally allows 3D synthesis from a single image.

As transformers are equivariant to the permutation of input tokens, encoding the positional information of tokens is necessary for many tasks. However, since existing positional encoding schemes have been initially designed for NLP tasks, their suitability for vision tasks, which typically exhibit different structural properties in their data, is questionable. We argue that existing positional encoding schemes are suboptimal for 3D vision tasks, as they do not respect their underlying 3D geometric structure. Based on this hypothesis, we propose a geometry-aware attention mechanism that encodes the geometric structure of tokens as relative transformation determined by the geometric relationship between queries and key-value pairs. By evaluating on multiple novel view synthesis (NVS) datasets in the sparse wide-baseline multi-view setting, we show that our attention, called Geometric Transform Attention (GTA), improves learning efficiency and performance of state-of-the-art transformer-based NVS models without any additional learned parameters and only minor computational overhead.

In document image rectification, there exist rich geometric constraints between the distorted image and the ground truth one. However, such geometric constraints are largely ignored in existing advanced solutions, which limits the rectification performance. To this end, we present DocGeoNet for document image rectification by introducing explicit geometric representation. Technically, two typical attributes of the document image are involved in the proposed geometric representation learning, i.e., 3D shape and textlines. Our motivation arises from the insight that 3D shape provides global unwarping cues for rectifying a distorted document image while overlooking the local structure. On the other hand, textlines complementarily provide explicit geometric constraints for local patterns. The learned geometric representation effectively bridges the distorted image and the ground truth one. Extensive experiments show the effectiveness of our framework and demonstrate the superiority of our DocGeoNet over state-of-the-art methods on both the DocUNet Benchmark dataset and our proposed DIR300 test set. The code is available at https://github.com/fh2019ustc/DocGeoNet.

Decision-based black-box attacks often necessitate a large number of queries to craft an adversarial example. Moreover, decision-based attacks based on querying boundary points in the estimated normal vector direction often suffer from inefficiency and convergence issues. In this paper, we propose a novel query-efficient curvature-aware geometric decision-based black-box attack (CGBA) that conducts boundary search along a semicircular path on a restricted 2D plane to ensure finding a boundary point successfully irrespective of the boundary curvature. While the proposed CGBA attack can work effectively for an arbitrary decision boundary, it is particularly efficient in exploiting the low curvature to craft high-quality adversarial examples, which is widely seen and experimentally verified in commonly used classifiers under non-targeted attacks. In contrast, the decision boundaries often exhibit higher curvature under targeted attacks. Thus, we develop a new query-efficient variant, CGBA-H, that is adapted for the targeted attack. In addition, we further design an algorithm to obtain a better initial boundary point at the expense of some extra queries, which considerably enhances the performance of the targeted attack. Extensive experiments are conducted to evaluate the performance of our proposed methods against some well-known classifiers on the ImageNet and CIFAR10 datasets, demonstrating the superiority of CGBA and CGBA-H over state-of-the-art non-targeted and targeted attacks, respectively. The source code is available at https://github.com/Farhamdur/CGBA.

With the goal of understanding the visual concepts that CLIP associates with text prompts, we show that the latent space of CLIP can be visualized solely in terms of linear transformations on simple geometric primitives like circles and straight lines. Although existing approaches achieve this by sketch-synthesis-through-optimization, they do so on the space of B\'ezier curves, which exhibit a wastefully large set of structures that they can evolve into, as most of them are non-essential for generating meaningful sketches. We present CLIPDrawX, an algorithm that provides significantly better visualizations for CLIP text embeddings, using only simple primitive shapes like straight lines and circles. This constrains the set of possible outputs to linear transformations on these primitives, thereby exhibiting an inherently simpler mathematical form. The synthesis process of CLIPDrawX can be tracked end-to-end, with each visual concept being explained exclusively in terms of primitives. Implementation will be released upon acceptance. Project Page: https://clipdrawx.github.io/{https://clipdrawx.github.io/}.

Generating high-quality 3D objects from textual descriptions remains a challenging problem due to computational cost, the scarcity of 3D data, and complex 3D representations. We introduce Geometry Image Diffusion (GIMDiffusion), a novel Text-to-3D model that utilizes geometry images to efficiently represent 3D shapes using 2D images, thereby avoiding the need for complex 3D-aware architectures. By integrating a Collaborative Control mechanism, we exploit the rich 2D priors of existing Text-to-Image models such as Stable Diffusion. This enables strong generalization even with limited 3D training data (allowing us to use only high-quality training data) as well as retaining compatibility with guidance techniques such as IPAdapter. In short, GIMDiffusion enables the generation of 3D assets at speeds comparable to current Text-to-Image models. The generated objects consist of semantically meaningful, separate parts and include internal structures, enhancing both usability and versatility.

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they enforce symmetries via the model architecture, which often reduces their expressivity, scalability and comprehensibility. In this paper, we introduce (1) a flexible framework relying on stochastic frame-averaging (SFA) to make any model E(3)-equivariant or invariant through data transformations. (2) FAENet: a simple, fast and expressive GNN, optimized for SFA, that processes geometric information without any symmetrypreserving design constraints. We prove the validity of our method theoretically and empirically demonstrate its superior accuracy and computational scalability in materials modeling on the OC20 dataset (S2EF, IS2RE) as well as common molecular modeling tasks (QM9, QM7-X). A package implementation is available at https://faenet.readthedocs.io.

3D-aware Generative Adversarial Networks (GANs) have shown remarkable progress in learning to generate multi-view-consistent images and 3D geometries of scenes from collections of 2D images via neural volume rendering. Yet, the significant memory and computational costs of dense sampling in volume rendering have forced 3D GANs to adopt patch-based training or employ low-resolution rendering with post-processing 2D super resolution, which sacrifices multiview consistency and the quality of resolved geometry. Consequently, 3D GANs have not yet been able to fully resolve the rich 3D geometry present in 2D images. In this work, we propose techniques to scale neural volume rendering to the much higher resolution of native 2D images, thereby resolving fine-grained 3D geometry with unprecedented detail. Our approach employs learning-based samplers for accelerating neural rendering for 3D GAN training using up to 5 times fewer depth samples. This enables us to explicitly "render every pixel" of the full-resolution image during training and inference without post-processing superresolution in 2D. Together with our strategy to learn high-quality surface geometry, our method synthesizes high-resolution 3D geometry and strictly view-consistent images while maintaining image quality on par with baselines relying on post-processing super resolution. We demonstrate state-of-the-art 3D gemetric quality on FFHQ and AFHQ, setting a new standard for unsupervised learning of 3D shapes in 3D GANs.

Despite recent advances in multimodal content generation enabled by vision-language models (VLMs), their ability to reason about and generate structured 3D scenes remains largely underexplored. This limitation constrains their utility in spatially grounded tasks such as embodied AI, immersive simulations, and interactive 3D applications. We introduce a new paradigm that enables VLMs to generate, understand, and edit complex 3D environments by injecting a continually evolving spatial context. Constructed from multimodal input, this context consists of three components: a scene portrait that provides a high-level semantic blueprint, a semantically labeled point cloud capturing object-level geometry, and a scene hypergraph that encodes rich spatial relationships, including unary, binary, and higher-order constraints. Together, these components provide the VLM with a structured, geometry-aware working memory that integrates its inherent multimodal reasoning capabilities with structured 3D understanding for effective spatial reasoning. Building on this foundation, we develop an agentic 3D scene generation pipeline in which the VLM iteratively reads from and updates the spatial context. The pipeline features high-quality asset generation with geometric restoration, environment setup with automatic verification, and ergonomic adjustment guided by the scene hypergraph. Experiments show that our framework can handle diverse and challenging inputs, achieving a level of generalization not observed in prior work. Further results demonstrate that injecting spatial context enables VLMs to perform downstream tasks such as interactive scene editing and path planning, suggesting strong potential for spatially intelligent systems in computer graphics, 3D vision, and embodied applications.

Novel view synthesis has demonstrated impressive progress recently, with 3D Gaussian splatting (3DGS) offering efficient training time and photorealistic real-time rendering. However, reliance on Cartesian coordinates limits 3DGS's performance on distant objects, which is important for reconstructing unbounded outdoor environments. We found that, despite its ultimate simplicity, using homogeneous coordinates, a concept on the projective geometry, for the 3DGS pipeline remarkably improves the rendering accuracies of distant objects. We therefore propose Homogeneous Gaussian Splatting (HoGS) incorporating homogeneous coordinates into the 3DGS framework, providing a unified representation for enhancing near and distant objects. HoGS effectively manages both expansive spatial positions and scales particularly in outdoor unbounded environments by adopting projective geometry principles. Experiments show that HoGS significantly enhances accuracy in reconstructing distant objects while maintaining high-quality rendering of nearby objects, along with fast training speed and real-time rendering capability. Our implementations are available on our project page https://kh129.github.io/hogs/.

Deep neural networks are prone to adversarial examples that maliciously alter the network's outcome. Due to the increasing popularity of 3D sensors in safety-critical systems and the vast deployment of deep learning models for 3D point sets, there is a growing interest in adversarial attacks and defenses for such models. So far, the research has focused on the semantic level, namely, deep point cloud classifiers. However, point clouds are also widely used in a geometric-related form that includes encoding and reconstructing the geometry. In this work, we are the first to consider the problem of adversarial examples at a geometric level. In this setting, the question is how to craft a small change to a clean source point cloud that leads, after passing through an autoencoder model, to the reconstruction of a different target shape. Our attack is in sharp contrast to existing semantic attacks on 3D point clouds. While such works aim to modify the predicted label by a classifier, we alter the entire reconstructed geometry. Additionally, we demonstrate the robustness of our attack in the case of defense, where we show that remnant characteristics of the target shape are still present at the output after applying the defense to the adversarial input. Our code is publicly available at https://github.com/itailang/geometric_adv.

3D textured face reconstruction from sketches applicable in many scenarios such as animation, 3D avatars, artistic design, missing people search, etc., is a highly promising but underdeveloped research topic. On the one hand, the stylistic diversity of sketches leads to existing sketch-to-3D-face methods only being able to handle pose-limited and realistically shaded sketches. On the other hand, texture plays a vital role in representing facial appearance, yet sketches lack this information, necessitating additional texture control in the reconstruction process. This paper proposes a novel method for reconstructing controllable textured and detailed 3D faces from sketches, named S2TD-Face. S2TD-Face introduces a two-stage geometry reconstruction framework that directly reconstructs detailed geometry from the input sketch. To keep geometry consistent with the delicate strokes of the sketch, we propose a novel sketch-to-geometry loss that ensures the reconstruction accurately fits the input features like dimples and wrinkles. Our training strategies do not rely on hard-to-obtain 3D face scanning data or labor-intensive hand-drawn sketches. Furthermore, S2TD-Face introduces a texture control module utilizing text prompts to select the most suitable textures from a library and seamlessly integrate them into the geometry, resulting in a 3D detailed face with controllable texture. S2TD-Face surpasses existing state-of-the-art methods in extensive quantitative and qualitative experiments. Our project is available at https://github.com/wang-zidu/S2TD-Face .

Existing Large Multimodal Models (LMMs) struggle with mathematical geometric reasoning due to a lack of high-quality image-text paired data. Current geometric data generation approaches, which apply preset templates to generate geometric data or use Large Language Models (LLMs) to rephrase questions and answers (Q&A), unavoidably limit data accuracy and diversity. To synthesize higher-quality data, we propose a two-stage Reverse Chain-of-Thought (R-CoT) geometry problem generation pipeline. First, we introduce GeoChain to produce high-fidelity geometric images and corresponding descriptions highlighting relations among geometric elements. We then design a Reverse A&Q method that reasons step-by-step based on the descriptions and generates questions in reverse from the reasoning results. Experiments demonstrate that the proposed method brings significant and consistent improvements on multiple LMM baselines, achieving new performance records in the 2B, 7B, and 8B settings. Notably, R-CoT-8B significantly outperforms previous state-of-the-art open-source mathematical models by 16.6% on MathVista and 9.2% on GeoQA, while also surpassing the closed-source model GPT-4o by an average of 13% across both datasets. The code is available at https://github.com/dle666/R-CoT.

The topic of stitching images with globally natural structures holds paramount significance. Current methodologies exhibit the ability to preserve local geometric structures, yet fall short in maintaining relationships between these geometric structures. In this paper, we endeavor to safeguard the overall, OBJect-level structures within images based on Global Similarity Prior, while concurrently mitigating distortion and ghosting artifacts with OBJ-GSP. Our approach leverages the Segment Anything Model to extract geometric structures with semantic information, enhancing the algorithm's ability to preserve objects in a manner that aligns more intuitively with human perception. We seek to identify spatial constraints that govern the relationships between various geometric boundaries. Recognizing that multiple geometric boundaries collectively define complete objects, we employ triangular meshes to safeguard not only individual geometric structures but also the overall shapes of objects within the images. Empirical evaluations across multiple image stitching datasets demonstrate that our method establishes a new state-of-the-art benchmark in image stitching. Our implementation and dataset is publicly available at https://github.com/RussRobin/OBJ-GSP .

Despite remarkable advancements in video depth estimation, existing methods exhibit inherent limitations in achieving geometric fidelity through the affine-invariant predictions, limiting their applicability in reconstruction and other metrically grounded downstream tasks. We propose GeometryCrafter, a novel framework that recovers high-fidelity point map sequences with temporal coherence from open-world videos, enabling accurate 3D/4D reconstruction, camera parameter estimation, and other depth-based applications. At the core of our approach lies a point map Variational Autoencoder (VAE) that learns a latent space agnostic to video latent distributions for effective point map encoding and decoding. Leveraging the VAE, we train a video diffusion model to model the distribution of point map sequences conditioned on the input videos. Extensive evaluations on diverse datasets demonstrate that GeometryCrafter achieves state-of-the-art 3D accuracy, temporal consistency, and generalization capability.

Triangle meshes are fundamental to 3D applications, enabling efficient modification and rasterization while maintaining compatibility with standard rendering pipelines. However, current automatic mesh generation methods typically rely on intermediate representations that lack the continuous surface quality inherent to meshes. Converting these representations into meshes produces dense, suboptimal outputs. Although recent autoregressive approaches demonstrate promise in directly modeling mesh vertices and faces, they are constrained by the limitation in face count, scalability, and structural fidelity. To address these challenges, we propose Nautilus, a locality-aware autoencoder for artist-like mesh generation that leverages the local properties of manifold meshes to achieve structural fidelity and efficient representation. Our approach introduces a novel tokenization algorithm that preserves face proximity relationships and compresses sequence length through locally shared vertices and edges, enabling the generation of meshes with an unprecedented scale of up to 5,000 faces. Furthermore, we develop a Dual-stream Point Conditioner that provides multi-scale geometric guidance, ensuring global consistency and local structural fidelity by capturing fine-grained geometric features. Extensive experiments demonstrate that Nautilus significantly outperforms state-of-the-art methods in both fidelity and scalability. The project page is at https://nautilusmeshgen.github.io.

A triangular mesh is one of the most popular 3D data representations. As such, the deployment of deep neural networks for mesh processing is widely spread and is increasingly attracting more attention. However, neural networks are prone to adversarial attacks, where carefully crafted inputs impair the model's functionality. The need to explore these vulnerabilities is a fundamental factor in the future development of 3D-based applications. Recently, mesh attacks were studied on the semantic level, where classifiers are misled to produce wrong predictions. Nevertheless, mesh surfaces possess complex geometric attributes beyond their semantic meaning, and their analysis often includes the need to encode and reconstruct the geometry of the shape. We propose a novel framework for a geometric adversarial attack on a 3D mesh autoencoder. In this setting, an adversarial input mesh deceives the autoencoder by forcing it to reconstruct a different geometric shape at its output. The malicious input is produced by perturbing a clean shape in the spectral domain. Our method leverages the spectral decomposition of the mesh along with additional mesh-related properties to obtain visually credible results that consider the delicacy of surface distortions. Our code is publicly available at https://github.com/StolikTomer/SAGA.

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the Pin(p,q,r) group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable geometric templates that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

We present DreamPolisher, a novel Gaussian Splatting based method with geometric guidance, tailored to learn cross-view consistency and intricate detail from textual descriptions. While recent progress on text-to-3D generation methods have been promising, prevailing methods often fail to ensure view-consistency and textural richness. This problem becomes particularly noticeable for methods that work with text input alone. To address this, we propose a two-stage Gaussian Splatting based approach that enforces geometric consistency among views. Initially, a coarse 3D generation undergoes refinement via geometric optimization. Subsequently, we use a ControlNet driven refiner coupled with the geometric consistency term to improve both texture fidelity and overall consistency of the generated 3D asset. Empirical evaluations across diverse textual prompts spanning various object categories demonstrate the efficacy of DreamPolisher in generating consistent and realistic 3D objects, aligning closely with the semantics of the textual instructions.

Predominant techniques on talking head generation largely depend on 2D information, including facial appearances and motions from input face images. Nevertheless, dense 3D facial geometry, such as pixel-wise depth, plays a critical role in constructing accurate 3D facial structures and suppressing complex background noises for generation. However, dense 3D annotations for facial videos is prohibitively costly to obtain. In this work, firstly, we present a novel self-supervised method for learning dense 3D facial geometry (ie, depth) from face videos, without requiring camera parameters and 3D geometry annotations in training. We further propose a strategy to learn pixel-level uncertainties to perceive more reliable rigid-motion pixels for geometry learning. Secondly, we design an effective geometry-guided facial keypoint estimation module, providing accurate keypoints for generating motion fields. Lastly, we develop a 3D-aware cross-modal (ie, appearance and depth) attention mechanism, which can be applied to each generation layer, to capture facial geometries in a coarse-to-fine manner. Extensive experiments are conducted on three challenging benchmarks (ie, VoxCeleb1, VoxCeleb2, and HDTF). The results demonstrate that our proposed framework can generate highly realistic-looking reenacted talking videos, with new state-of-the-art performances established on these benchmarks. The codes and trained models are publicly available on the GitHub project page at https://github.com/harlanhong/CVPR2022-DaGAN

Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets. Therefore, in order to expand the transfer learning scheme to regression tasks, we propose a novel transfer technique based on differential geometry, namely the Geometrically Aligned Transfer Encoder (GATE). In this method, we interpret the latent vectors from the model to exist on a Riemannian curved manifold. We find a proper diffeomorphism between pairs of tasks to ensure that every arbitrary point maps to a locally flat coordinate in the overlapping region, allowing the transfer of knowledge from the source to the target data. This also serves as an effective regularizer for the model to behave in extrapolation regions. In this article, we demonstrate that GATE outperforms conventional methods and exhibits stable behavior in both the latent space and extrapolation regions for various molecular graph datasets.

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is unlimited in resolution. Unfortunately, these methods are often unsuitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Implicit Fields. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define DeepMesh - an end-to-end differentiable mesh representation that can vary its topology. We validate our theoretical insight through several applications: Single view 3D Reconstruction via Differentiable Rendering, Physically-Driven Shape Optimization, Full Scene 3D Reconstruction from Scans and End-to-End Training. In all cases our end-to-end differentiable parameterization gives us an edge over state-of-the-art algorithms.

3D Gaussian Splatting has recently achieved notable success in novel view synthesis for dynamic scenes and geometry reconstruction in static scenes. Building on these advancements, early methods have been developed for dynamic surface reconstruction by globally optimizing entire sequences. However, reconstructing dynamic scenes with significant topology changes, emerging or disappearing objects, and rapid movements remains a substantial challenge, particularly for long sequences. To address these issues, we propose AT-GS, a novel method for reconstructing high-quality dynamic surfaces from multi-view videos through per-frame incremental optimization. To avoid local minima across frames, we introduce a unified and adaptive gradient-aware densification strategy that integrates the strengths of conventional cloning and splitting techniques. Additionally, we reduce temporal jittering in dynamic surfaces by ensuring consistency in curvature maps across consecutive frames. Our method achieves superior accuracy and temporal coherence in dynamic surface reconstruction, delivering high-fidelity space-time novel view synthesis, even in complex and challenging scenes. Extensive experiments on diverse multi-view video datasets demonstrate the effectiveness of our approach, showing clear advantages over baseline methods. Project page: https://fraunhoferhhi.github.io/AT-GS

In this work, instead of directly predicting the pixel-level segmentation masks, the problem of referring image segmentation is formulated as sequential polygon generation, and the predicted polygons can be later converted into segmentation masks. This is enabled by a new sequence-to-sequence framework, Polygon Transformer (PolyFormer), which takes a sequence of image patches and text query tokens as input, and outputs a sequence of polygon vertices autoregressively. For more accurate geometric localization, we propose a regression-based decoder, which predicts the precise floating-point coordinates directly, without any coordinate quantization error. In the experiments, PolyFormer outperforms the prior art by a clear margin, e.g., 5.40% and 4.52% absolute improvements on the challenging RefCOCO+ and RefCOCOg datasets. It also shows strong generalization ability when evaluated on the referring video segmentation task without fine-tuning, e.g., achieving competitive 61.5% J&F on the Ref-DAVIS17 dataset.

General object composition (GOC) aims to seamlessly integrate a target object into a background scene with desired geometric properties, while simultaneously preserving its fine-grained appearance details. Recent approaches derive semantic embeddings and integrate them into advanced diffusion models to enable geometry-editable generation. However, these highly compact embeddings encode only high-level semantic cues and inevitably discard fine-grained appearance details. We introduce a Disentangled Geometry-editable and Appearance-preserving Diffusion (DGAD) model that first leverages semantic embeddings to implicitly capture the desired geometric transformations and then employs a cross-attention retrieval mechanism to align fine-grained appearance features with the geometry-edited representation, facilitating both precise geometry editing and faithful appearance preservation in object composition. Specifically, DGAD builds on CLIP/DINO-derived and reference networks to extract semantic embeddings and appearance-preserving representations, which are then seamlessly integrated into the encoding and decoding pipelines in a disentangled manner. We first integrate the semantic embeddings into pre-trained diffusion models that exhibit strong spatial reasoning capabilities to implicitly capture object geometry, thereby facilitating flexible object manipulation and ensuring effective editability. Then, we design a dense cross-attention mechanism that leverages the implicitly learned object geometry to retrieve and spatially align appearance features with their corresponding regions, ensuring faithful appearance consistency. Extensive experiments on public benchmarks demonstrate the effectiveness of the proposed DGAD framework.

Text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models has shown great promise but still suffers from inconsistent 3D geometric structures (Janus problems) and severe artifacts. The aforementioned problems mainly stem from 2D diffusion models lacking 3D awareness during the lifting. In this work, we present GeoDream, a novel method that incorporates explicit generalized 3D priors with 2D diffusion priors to enhance the capability of obtaining unambiguous 3D consistent geometric structures without sacrificing diversity or fidelity. Specifically, we first utilize a multi-view diffusion model to generate posed images and then construct cost volume from the predicted image, which serves as native 3D geometric priors, ensuring spatial consistency in 3D space. Subsequently, we further propose to harness 3D geometric priors to unlock the great potential of 3D awareness in 2D diffusion priors via a disentangled design. Notably, disentangling 2D and 3D priors allows us to refine 3D geometric priors further. We justify that the refined 3D geometric priors aid in the 3D-aware capability of 2D diffusion priors, which in turn provides superior guidance for the refinement of 3D geometric priors. Our numerical and visual comparisons demonstrate that GeoDream generates more 3D consistent textured meshes with high-resolution realistic renderings (i.e., 1024 times 1024) and adheres more closely to semantic coherence.

Text-to-3D generation represents an exciting field that has seen rapid advancements, facilitating the transformation of textual descriptions into detailed 3D models. However, current progress often neglects the intricate high-order correlation of geometry and texture within 3D objects, leading to challenges such as over-smoothness, over-saturation and the Janus problem. In this work, we propose a method named ``3D Gaussian Generation via Hypergraph (Hyper-3DG)'', designed to capture the sophisticated high-order correlations present within 3D objects. Our framework is anchored by a well-established mainflow and an essential module, named ``Geometry and Texture Hypergraph Refiner (HGRefiner)''. This module not only refines the representation of 3D Gaussians but also accelerates the update process of these 3D Gaussians by conducting the Patch-3DGS Hypergraph Learning on both explicit attributes and latent visual features. Our framework allows for the production of finely generated 3D objects within a cohesive optimization, effectively circumventing degradation. Extensive experimentation has shown that our proposed method significantly enhances the quality of 3D generation while incurring no additional computational overhead for the underlying framework. (Project code: https://github.com/yjhboy/Hyper3DG)

Recent advances in scene understanding benefit a lot from depth maps because of the 3D geometry information, especially in complex conditions (e.g., low light and overexposed). Existing approaches encode depth maps along with RGB images and perform feature fusion between them to enable more robust predictions. Taking into account that depth can be regarded as a geometry supplement for RGB images, a straightforward question arises: Do we really need to explicitly encode depth information with neural networks as done for RGB images? Based on this insight, in this paper, we investigate a new way to learn RGBD feature representations and present DFormerv2, a strong RGBD encoder that explicitly uses depth maps as geometry priors rather than encoding depth information with neural networks. Our goal is to extract the geometry clues from the depth and spatial distances among all the image patch tokens, which will then be used as geometry priors to allocate attention weights in self-attention. Extensive experiments demonstrate that DFormerv2 exhibits exceptional performance in various RGBD semantic segmentation benchmarks. Code is available at: https://github.com/VCIP-RGBD/DFormer.

3D understanding and rendering of moving humans from monocular videos is a challenging task. Despite recent progress, the task remains difficult in real-world scenarios, where obstacles may block the camera view and cause partial occlusions in the captured videos. Existing methods cannot handle such defects due to two reasons. First, the standard rendering strategy relies on point-point mapping, which could lead to dramatic disparities between the visible and occluded areas of the body. Second, the naive direct regression approach does not consider any feasibility criteria (ie, prior information) for rendering under occlusions. To tackle the above drawbacks, we present OccNeRF, a neural rendering method that achieves better rendering of humans in severely occluded scenes. As direct solutions to the two drawbacks, we propose surface-based rendering by integrating geometry and visibility priors. We validate our method on both simulated and real-world occlusions and demonstrate our method's superiority.

Geometric Deep Learning has recently made striking progress with the advent of continuous Deep Implicit Fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is not limited in resolution. Unfortunately, these methods are often not suitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Signed Distance Functions. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define MeshSDF, an end-to-end differentiable mesh representation which can vary its topology. We use two different applications to validate our theoretical insight: Single-View Reconstruction via Differentiable Rendering and Physically-Driven Shape Optimization. In both cases our differentiable parameterization gives us an edge over state-of-the-art algorithms.

Colorizing line art is a pivotal task in the production of hand-drawn cel animation. This typically involves digital painters using a paint bucket tool to manually color each segment enclosed by lines, based on RGB values predetermined by a color designer. This frame-by-frame process is both arduous and time-intensive. Current automated methods mainly focus on segment matching. This technique migrates colors from a reference to the target frame by aligning features within line-enclosed segments across frames. However, issues like occlusion and wrinkles in animations often disrupt these direct correspondences, leading to mismatches. In this work, we introduce a new learning-based inclusion matching pipeline, which directs the network to comprehend the inclusion relationships between segments rather than relying solely on direct visual correspondences. Our method features a two-stage pipeline that integrates a coarse color warping module with an inclusion matching module, enabling more nuanced and accurate colorization. To facilitate the training of our network, we also develope a unique dataset, referred to as PaintBucket-Character. This dataset includes rendered line arts alongside their colorized counterparts, featuring various 3D characters. Extensive experiments demonstrate the effectiveness and superiority of our method over existing techniques.

Automatic 3D content creation has achieved rapid progress recently due to the availability of pre-trained, large language models and image diffusion models, forming the emerging topic of text-to-3D content creation. Existing text-to-3D methods commonly use implicit scene representations, which couple the geometry and appearance via volume rendering and are suboptimal in terms of recovering finer geometries and achieving photorealistic rendering; consequently, they are less effective for generating high-quality 3D assets. In this work, we propose a new method of Fantasia3D for high-quality text-to-3D content creation. Key to Fantasia3D is the disentangled modeling and learning of geometry and appearance. For geometry learning, we rely on a hybrid scene representation, and propose to encode surface normal extracted from the representation as the input of the image diffusion model. For appearance modeling, we introduce the spatially varying bidirectional reflectance distribution function (BRDF) into the text-to-3D task, and learn the surface material for photorealistic rendering of the generated surface. Our disentangled framework is more compatible with popular graphics engines, supporting relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments that show the advantages of our method over existing ones under different text-to-3D task settings. Project page and source codes: https://fantasia3d.github.io/.

Monocular object pose estimation, as a pivotal task in computer vision and robotics, heavily depends on accurate 2D-3D correspondences, which often demand costly CAD models that may not be readily available. Object 3D reconstruction methods offer an alternative, among which recent advancements in 3D Gaussian Splatting (3DGS) afford a compelling potential. Yet its performance still suffers and tends to overfit with fewer input views. Embracing this challenge, we introduce SGPose, a novel framework for sparse view object pose estimation using Gaussian-based methods. Given as few as ten views, SGPose generates a geometric-aware representation by starting with a random cuboid initialization, eschewing reliance on Structure-from-Motion (SfM) pipeline-derived geometry as required by traditional 3DGS methods. SGPose removes the dependence on CAD models by regressing dense 2D-3D correspondences between images and the reconstructed model from sparse input and random initialization, while the geometric-consistent depth supervision and online synthetic view warping are key to the success. Experiments on typical benchmarks, especially on the Occlusion LM-O dataset, demonstrate that SGPose outperforms existing methods even under sparse view constraints, under-scoring its potential in real-world applications.

Efficiently synthesizing novel views from sparse inputs while maintaining accuracy remains a critical challenge in 3D reconstruction. While advanced techniques like radiance fields and 3D Gaussian Splatting achieve rendering quality and impressive efficiency with dense view inputs, they suffer from significant geometric reconstruction errors when applied to sparse input views. Moreover, although recent methods leverage monocular depth estimation to enhance geometric learning, their dependence on single-view estimated depth often leads to view inconsistency issues across different viewpoints. Consequently, this reliance on absolute depth can introduce inaccuracies in geometric information, ultimately compromising the quality of scene reconstruction with Gaussian splats. In this paper, we present RDG-GS, a novel sparse-view 3D rendering framework with Relative Depth Guidance based on 3D Gaussian Splatting. The core innovation lies in utilizing relative depth guidance to refine the Gaussian field, steering it towards view-consistent spatial geometric representations, thereby enabling the reconstruction of accurate geometric structures and capturing intricate textures. First, we devise refined depth priors to rectify the coarse estimated depth and insert global and fine-grained scene information to regular Gaussians. Building on this, to address spatial geometric inaccuracies from absolute depth, we propose relative depth guidance by optimizing the similarity between spatially correlated patches of depth and images. Additionally, we also directly deal with the sparse areas challenging to converge by the adaptive sampling for quick densification. Across extensive experiments on Mip-NeRF360, LLFF, DTU, and Blender, RDG-GS demonstrates state-of-the-art rendering quality and efficiency, making a significant advancement for real-world application.

The Multiplane Image (MPI), containing a set of fronto-parallel RGBA layers, is an effective and efficient representation for view synthesis from sparse inputs. Yet, its fixed structure limits the performance, especially for surfaces imaged at oblique angles. We introduce the Structural MPI (S-MPI), where the plane structure approximates 3D scenes concisely. Conveying RGBA contexts with geometrically-faithful structures, the S-MPI directly bridges view synthesis and 3D reconstruction. It can not only overcome the critical limitations of MPI, i.e., discretization artifacts from sloped surfaces and abuse of redundant layers, and can also acquire planar 3D reconstruction. Despite the intuition and demand of applying S-MPI, great challenges are introduced, e.g., high-fidelity approximation for both RGBA layers and plane poses, multi-view consistency, non-planar regions modeling, and efficient rendering with intersected planes. Accordingly, we propose a transformer-based network based on a segmentation model. It predicts compact and expressive S-MPI layers with their corresponding masks, poses, and RGBA contexts. Non-planar regions are inclusively handled as a special case in our unified framework. Multi-view consistency is ensured by sharing global proxy embeddings, which encode plane-level features covering the complete 3D scenes with aligned coordinates. Intensive experiments show that our method outperforms both previous state-of-the-art MPI-based view synthesis methods and planar reconstruction methods.

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of geometric deep learning. Often problems in the physical sciences deal with relatively small sets of points in two- or three-dimensional space wherein translation, rotation, and permutation equivariance are important or even vital for models to be useful in practice. In this work, we present rotation- and permutation-equivariant architectures for deep learning on these small point clouds, composed of a set of products of terms from the geometric algebra and reductions over those products using an attention mechanism. The geometric algebra provides valuable mathematical structure by which to combine vector, scalar, and other types of geometric inputs in a systematic way to account for rotation invariance or covariance, while attention yields a powerful way to impose permutation equivariance. We demonstrate the usefulness of these architectures by training models to solve sample problems relevant to physics, chemistry, and biology.

Brain-computer interfaces (BCIs) offer transformative potential, but decoding neural signals presents significant challenges. The core premise of this paper is built around demonstrating methods to elucidate the underlying low-dimensional geometric structure present in high-dimensional brainwave data in order to assist in downstream BCI-related neural classification tasks. We demonstrate two pipelines related to electroencephalography (EEG) signal processing: (1) a preliminary pipeline removing noise from individual EEG channels, and (2) a downstream manifold learning pipeline uncovering geometric structure across networks of EEG channels. We conduct preliminary validation using two EEG datasets and situate our demonstration in the context of the BCI-relevant imagined digit decoding problem. Our preliminary pipeline uses an attention-based EEG filtration network to extract clean signal from individual EEG channels. Our primary pipeline uses a fast Fourier transform, a Laplacian eigenmap, a discrete analog of Ricci flow via Ollivier's notion of Ricci curvature, and a graph convolutional network to perform dimensionality reduction on high-dimensional multi-channel EEG data in order to enable regularizable downstream classification. Our system achieves competitive performance with existing signal processing and classification benchmarks; we demonstrate a mean test correlation coefficient of >0.95 at 2 dB on semi-synthetic neural denoising and a downstream EEG-based classification accuracy of 0.97 on distinguishing digit- versus non-digit- thoughts. Results are preliminary and our geometric machine learning pipeline should be validated by more extensive follow-up studies; generalizing these results to larger inter-subject sample sizes, different hardware systems, and broader use cases will be crucial.

In the realm of vision models, the primary mode of representation is using pixels to rasterize the visual world. Yet this is not always the best or unique way to represent visual content, especially for designers and artists who depict the world using geometry primitives such as polygons. Vector graphics (VG), on the other hand, offer a textual representation of visual content, which can be more concise and powerful for content like cartoons or sketches. Recent studies have shown promising results on processing vector graphics with capable Large Language Models (LLMs). However, such works focus solely on qualitative results, understanding, or a specific type of vector graphics. We propose VGBench, a comprehensive benchmark for LLMs on handling vector graphics through diverse aspects, including (a) both visual understanding and generation, (b) evaluation of various vector graphics formats, (c) diverse question types, (d) wide range of prompting techniques, (e) under multiple LLMs. Evaluating on our collected 4279 understanding and 5845 generation samples, we find that LLMs show strong capability on both aspects while exhibiting less desirable performance on low-level formats (SVG). Both data and evaluation pipeline will be open-sourced at https://vgbench.github.io.

Scene generation with 3D assets presents a complex challenge, requiring both high-level semantic understanding and low-level geometric reasoning. While Multimodal Large Language Models (MLLMs) excel at semantic tasks, their application to 3D scene generation is hindered by their limited grounding on 3D geometry. In this paper, we investigate how to best work with MLLMs in an object placement task. Towards this goal, we introduce a novel framework, FirePlace, that applies existing MLLMs in (1) 3D geometric reasoning and the extraction of relevant geometric details from the 3D scene, (2) constructing and solving geometric constraints on the extracted low-level geometry, and (3) pruning for final placements that conform to common sense. By combining geometric reasoning with real-world understanding of MLLMs, our method can propose object placements that satisfy both geometric constraints as well as high-level semantic common-sense considerations. Our experiments show that these capabilities allow our method to place objects more effectively in complex scenes with intricate geometry, surpassing the quality of prior work.

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold using geodesic-guided flows. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.

Mesh quality assessment (MQA) models play a critical role in the design, optimization, and evaluation of mesh operation systems in a wide variety of applications. Current MQA models, whether model-based methods using topology-aware features or projection-based approaches working on rendered 2D projections, often fail to capture the intricate interactions between texture and 3D geometry. We introduce HybridMQA, a first-of-its-kind hybrid full-reference colored MQA framework that integrates model-based and projection-based approaches, capturing complex interactions between textural information and 3D structures for enriched quality representations. Our method employs graph learning to extract detailed 3D representations, which are then projected to 2D using a novel feature rendering process that precisely aligns them with colored projections. This enables the exploration of geometry-texture interactions via cross-attention, producing comprehensive mesh quality representations. Extensive experiments demonstrate HybridMQA's superior performance across diverse datasets, highlighting its ability to effectively leverage geometry-texture interactions for a thorough understanding of mesh quality. Our implementation will be made publicly available.

In this paper, we present CAD2Program, a new method for reconstructing 3D parametric models from 2D CAD drawings. Our proposed method is inspired by recent successes in vision-language models (VLMs), and departs from traditional methods which rely on task-specific data representations and/or algorithms. Specifically, on the input side, we simply treat the 2D CAD drawing as a raster image, regardless of its original format, and encode the image with a standard ViT model. We show that such an encoding scheme achieves competitive performance against existing methods that operate on vector-graphics inputs, while imposing substantially fewer restrictions on the 2D drawings. On the output side, our method auto-regressively predicts a general-purpose language describing 3D parametric models in text form. Compared to other sequence modeling methods for CAD which use domain-specific sequence representations with fixed-size slots, our text-based representation is more flexible, and can be easily extended to arbitrary geometric entities and semantic or functional properties. Experimental results on a large-scale dataset of cabinet models demonstrate the effectiveness of our method.

Diffusion-based text-to-image models ignited immense attention from the vision community, artists, and content creators. Broad adoption of these models is due to significant improvement in the quality of generations and efficient conditioning on various modalities, not just text. However, lifting the rich generative priors of these 2D models into 3D is challenging. Recent works have proposed various pipelines powered by the entanglement of diffusion models and neural fields. We explore the power of pretrained 2D diffusion models and standard 3D neural radiance fields as independent, standalone tools and demonstrate their ability to work together in a non-learned fashion. Such modularity has the intrinsic advantage of eased partial upgrades, which became an important property in such a fast-paced domain. Our pipeline accepts any legacy renderable geometry, such as textured or untextured meshes, orchestrates the interaction between 2D generative refinement and 3D consistency enforcement tools, and outputs a painted input geometry in several formats. We conduct a large-scale study on a wide range of objects and categories from the ShapeNetSem dataset and demonstrate the advantages of our approach, both qualitatively and quantitatively. Project page: https://www.obukhov.ai/repainting_3d_assets

3D Gaussian Splatting (3DGS) has recently attracted wide attentions in various areas such as 3D navigation, Virtual Reality (VR) and 3D simulation, due to its photorealistic and efficient rendering performance. High-quality reconstrution of 3DGS relies on sufficient splats and a reasonable distribution of these splats to fit real geometric surface and texture details, which turns out to be a challenging problem. We present GeoTexDensifier, a novel geometry-texture-aware densification strategy to reconstruct high-quality Gaussian splats which better comply with the geometric structure and texture richness of the scene. Specifically, our GeoTexDensifier framework carries out an auxiliary texture-aware densification method to produce a denser distribution of splats in fully textured areas, while keeping sparsity in low-texture regions to maintain the quality of Gaussian point cloud. Meanwhile, a geometry-aware splitting strategy takes depth and normal priors to guide the splitting sampling and filter out the noisy splats whose initial positions are far from the actual geometric surfaces they aim to fit, under a Validation of Depth Ratio Change checking. With the help of relative monocular depth prior, such geometry-aware validation can effectively reduce the influence of scattered Gaussians to the final rendering quality, especially in regions with weak textures or without sufficient training views. The texture-aware densification and geometry-aware splitting strategies are fully combined to obtain a set of high-quality Gaussian splats. We experiment our GeoTexDensifier framework on various datasets and compare our Novel View Synthesis results to other state-of-the-art 3DGS approaches, with detailed quantitative and qualitative evaluations to demonstrate the effectiveness of our method in producing more photorealistic 3DGS models.

Understanding the 3D semantics of a scene is a fundamental problem for various scenarios such as embodied agents. While NeRFs and 3DGS excel at novel-view synthesis, previous methods for understanding their semantics have been limited to incomplete 3D understanding: their segmentation results are 2D masks and their supervision is anchored at 2D pixels. This paper revisits the problem set to pursue a better 3D understanding of a scene modeled by NeRFs and 3DGS as follows. 1) We directly supervise the 3D points to train the language embedding field. It achieves state-of-the-art accuracy without relying on multi-scale language embeddings. 2) We transfer the pre-trained language field to 3DGS, achieving the first real-time rendering speed without sacrificing training time or accuracy. 3) We introduce a 3D querying and evaluation protocol for assessing the reconstructed geometry and semantics together. Code, checkpoints, and annotations will be available online. Project page: https://hyunji12.github.io/Open3DRF

Embodied tasks require the agent to fully understand 3D scenes simultaneously with its exploration, so an online, real-time, fine-grained and highly-generalized 3D perception model is desperately needed. Since high-quality 3D data is limited, directly training such a model in 3D is almost infeasible. Meanwhile, vision foundation models (VFM) has revolutionized the field of 2D computer vision with superior performance, which makes the use of VFM to assist embodied 3D perception a promising direction. However, most existing VFM-assisted 3D perception methods are either offline or too slow that cannot be applied in practical embodied tasks. In this paper, we aim to leverage Segment Anything Model (SAM) for real-time 3D instance segmentation in an online setting. This is a challenging problem since future frames are not available in the input streaming RGB-D video, and an instance may be observed in several frames so object matching between frames is required. To address these challenges, we first propose a geometric-aware query lifting module to represent the 2D masks generated by SAM by 3D-aware queries, which is then iteratively refined by a dual-level query decoder. In this way, the 2D masks are transferred to fine-grained shapes on 3D point clouds. Benefit from the query representation for 3D masks, we can compute the similarity matrix between the 3D masks from different views by efficient matrix operation, which enables real-time inference. Experiments on ScanNet, ScanNet200, SceneNN and 3RScan show our method achieves leading performance even compared with offline methods. Our method also demonstrates great generalization ability in several zero-shot dataset transferring experiments and show great potential in open-vocabulary and data-efficient setting. Code and demo are available at https://xuxw98.github.io/ESAM/, with only one RTX 3090 GPU required for training and evaluation.

In this work, we recover the underlying 3D structure of non-geometrically consistent scenes. We focus our analysis on hand-drawn images from cartoons and anime. Many cartoons are created by artists without a 3D rendering engine, which means that any new image of a scene is hand-drawn. The hand-drawn images are usually faithful representations of the world, but only in a qualitative sense, since it is difficult for humans to draw multiple perspectives of an object or scene 3D consistently. Nevertheless, people can easily perceive 3D scenes from inconsistent inputs! In this work, we correct for 2D drawing inconsistencies to recover a plausible 3D structure such that the newly warped drawings are consistent with each other. Our pipeline consists of a user-friendly annotation tool, camera pose estimation, and image deformation to recover a dense structure. Our method warps images to obey a perspective camera model, enabling our aligned results to be plugged into novel-view synthesis reconstruction methods to experience cartoons from viewpoints never drawn before. Our project page is https://toon3d.studio/.

Large-scale text-to-image models enable a wide range of image editing techniques, using text prompts or even spatial controls. However, applying these editing methods to multi-view images depicting a single scene leads to 3D-inconsistent results. In this work, we focus on spatial control-based geometric manipulations and introduce a method to consolidate the editing process across various views. We build on two insights: (1) maintaining consistent features throughout the generative process helps attain consistency in multi-view editing, and (2) the queries in self-attention layers significantly influence the image structure. Hence, we propose to improve the geometric consistency of the edited images by enforcing the consistency of the queries. To do so, we introduce QNeRF, a neural radiance field trained on the internal query features of the edited images. Once trained, QNeRF can render 3D-consistent queries, which are then softly injected back into the self-attention layers during generation, greatly improving multi-view consistency. We refine the process through a progressive, iterative method that better consolidates queries across the diffusion timesteps. We compare our method to a range of existing techniques and demonstrate that it can achieve better multi-view consistency and higher fidelity to the input scene. These advantages allow us to train NeRFs with fewer visual artifacts, that are better aligned with the target geometry.

We propose a novel memory mechanism to build video generators that can explore environments interactively. Similar results have previously been achieved by out-painting 2D views of the scene while incrementally reconstructing its 3D geometry, which quickly accumulates errors, or by video generators with a short context window, which struggle to maintain scene coherence over the long term. To address these limitations, we introduce Surfel-Indexed View Memory (VMem), a mechanism that remembers past views by indexing them geometrically based on the 3D surface elements (surfels) they have observed. VMem enables the efficient retrieval of the most relevant past views when generating new ones. By focusing only on these relevant views, our method produces consistent explorations of imagined environments at a fraction of the computational cost of using all past views as context. We evaluate our approach on challenging long-term scene synthesis benchmarks and demonstrate superior performance compared to existing methods in maintaining scene coherence and camera control.

Due to high utility in many applications, from social networks to blockchain to power grids, deep learning on non-Euclidean objects such as graphs and manifolds, coined Geometric Deep Learning (GDL), continues to gain an ever increasing interest. We propose a new L\'evy Flights Graph Convolutional Networks (LFGCN) method for semi-supervised learning, which casts the L\'evy Flights into random walks on graphs and, as a result, allows both to accurately account for the intrinsic graph topology and to substantially improve classification performance, especially for heterogeneous graphs. Furthermore, we propose a new preferential P-DropEdge method based on the Girvan-Newman argument. That is, in contrast to uniform removing of edges as in DropEdge, following the Girvan-Newman algorithm, we detect network periphery structures using information on edge betweenness and then remove edges according to their betweenness centrality. Our experimental results on semi-supervised node classification tasks demonstrate that the LFGCN coupled with P-DropEdge accelerates the training task, increases stability and further improves predictive accuracy of learned graph topology structure. Finally, in our case studies we bring the machinery of LFGCN and other deep networks tools to analysis of power grid networks - the area where the utility of GDL remains untapped.

Geometric deep learning, i.e., designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, have achieved great successes in the last decade. One critical inductive bias is that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. The existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. To solve this problem, we revisit why the existing neural networks cannot maintain transformation invariance when handling geometric data. Our findings show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNN), a straightforward and general framework for geometric data. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling before feeding the representations into neural networks. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our proposed method. Based on the experimental results, we advocate that TinvNN should be considered a new starting point and an essential baseline for further studies of transformation-invariant geometric deep learning.

Real-time rendering and animation of humans is a core function in games, movies, and telepresence applications. Existing methods have a number of drawbacks we aim to address with our work. Triangle meshes have difficulty modeling thin structures like hair, volumetric representations like Neural Volumes are too low-resolution given a reasonable memory budget, and high-resolution implicit representations like Neural Radiance Fields are too slow for use in real-time applications. We present Mixture of Volumetric Primitives (MVP), a representation for rendering dynamic 3D content that combines the completeness of volumetric representations with the efficiency of primitive-based rendering, e.g., point-based or mesh-based methods. Our approach achieves this by leveraging spatially shared computation with a deconvolutional architecture and by minimizing computation in empty regions of space with volumetric primitives that can move to cover only occupied regions. Our parameterization supports the integration of correspondence and tracking constraints, while being robust to areas where classical tracking fails, such as around thin or translucent structures and areas with large topological variability. MVP is a hybrid that generalizes both volumetric and primitive-based representations. Through a series of extensive experiments we demonstrate that it inherits the strengths of each, while avoiding many of their limitations. We also compare our approach to several state-of-the-art methods and demonstrate that MVP produces superior results in terms of quality and runtime performance.

Adversarial threats against LLMs are escalating faster than current defenses can adapt. We expose a critical geometric blind spot in alignment: adversarial prompts exploit latent camouflage, embedding perilously close to the safe representation manifold while encoding unsafe intent thereby evading surface level defenses like Direct Preference Optimization (DPO), which remain blind to the latent geometry. We introduce ALKALI, the first rigorously curated adversarial benchmark and the most comprehensive to date spanning 9,000 prompts across three macro categories, six subtypes, and fifteen attack families. Evaluation of 21 leading LLMs reveals alarmingly high Attack Success Rates (ASRs) across both open and closed source models, exposing an underlying vulnerability we term latent camouflage, a structural blind spot where adversarial completions mimic the latent geometry of safe ones. To mitigate this vulnerability, we introduce GRACE - Geometric Representation Aware Contrastive Enhancement, an alignment framework coupling preference learning with latent space regularization. GRACE enforces two constraints: latent separation between safe and adversarial completions, and adversarial cohesion among unsafe and jailbreak behaviors. These operate over layerwise pooled embeddings guided by a learned attention profile, reshaping internal geometry without modifying the base model, and achieve up to 39% ASR reduction. Moreover, we introduce AVQI, a geometry aware metric that quantifies latent alignment failure via cluster separation and compactness. AVQI reveals when unsafe completions mimic the geometry of safe ones, offering a principled lens into how models internally encode safety. We make the code publicly available at https://anonymous.4open.science/r/alkali-B416/README.md.

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

Creating CAD digital twins from the physical world is crucial for manufacturing, design, and simulation. However, current methods typically rely on costly 3D scanning with labor-intensive post-processing. To provide a user-friendly design process, we explore the problem of reverse engineering from unconstrained real-world CAD images that can be easily captured by users of all experiences. However, the scarcity of real-world CAD data poses challenges in directly training such models. To tackle these challenges, we propose CADCrafter, an image-to-parametric CAD model generation framework that trains solely on synthetic textureless CAD data while testing on real-world images. To bridge the significant representation disparity between images and parametric CAD models, we introduce a geometry encoder to accurately capture diverse geometric features. Moreover, the texture-invariant properties of the geometric features can also facilitate the generalization to real-world scenarios. Since compiling CAD parameter sequences into explicit CAD models is a non-differentiable process, the network training inherently lacks explicit geometric supervision. To impose geometric validity constraints, we employ direct preference optimization (DPO) to fine-tune our model with the automatic code checker feedback on CAD sequence quality. Furthermore, we collected a real-world dataset, comprised of multi-view images and corresponding CAD command sequence pairs, to evaluate our method. Experimental results demonstrate that our approach can robustly handle real unconstrained CAD images, and even generalize to unseen general objects.

3D Gaussian Splatting (3DGS) has emerged as a powerful representation for real-time, high-performance rendering, enabling a wide range of applications. However, representing 3D scenes with numerous explicit Gaussian primitives imposes significant storage and memory overhead. Recent studies have shown that high-quality rendering can be achieved with a substantially reduced number of Gaussians when represented with high-precision attributes. Nevertheless, existing 3DGS compression methods still rely on a relatively large number of Gaussians, focusing primarily on attribute compression. This is because a smaller set of Gaussians becomes increasingly sensitive to lossy attribute compression, leading to severe quality degradation. Since the number of Gaussians is directly tied to computational costs, it is essential to reduce the number of Gaussians effectively rather than only optimizing storage. In this paper, we propose Optimized Minimal Gaussians representation (OMG), which significantly reduces storage while using a minimal number of primitives. First, we determine the distinct Gaussian from the near ones, minimizing redundancy without sacrificing quality. Second, we propose a compact and precise attribute representation that efficiently captures both continuity and irregularity among primitives. Additionally, we propose a sub-vector quantization technique for improved irregularity representation, maintaining fast training with a negligible codebook size. Extensive experiments demonstrate that OMG reduces storage requirements by nearly 50% compared to the previous state-of-the-art and enables 600+ FPS rendering while maintaining high rendering quality. Our source code is available at https://maincold2.github.io/omg/.

Neural Radiance Fields (NeRFs) have demonstrated amazing ability to synthesize images of 3D scenes from novel views. However, they rely upon specialized volumetric rendering algorithms based on ray marching that are mismatched to the capabilities of widely deployed graphics hardware. This paper introduces a new NeRF representation based on textured polygons that can synthesize novel images efficiently with standard rendering pipelines. The NeRF is represented as a set of polygons with textures representing binary opacities and feature vectors. Traditional rendering of the polygons with a z-buffer yields an image with features at every pixel, which are interpreted by a small, view-dependent MLP running in a fragment shader to produce a final pixel color. This approach enables NeRFs to be rendered with the traditional polygon rasterization pipeline, which provides massive pixel-level parallelism, achieving interactive frame rates on a wide range of compute platforms, including mobile phones.

Text-to-3D generation from a single-view image is a popular but challenging task in 3D vision. Although numerous methods have been proposed, existing works still suffer from the inconsistency issues, including 1) semantic inconsistency, 2) geometric inconsistency, and 3) saturation inconsistency, resulting in distorted, overfitted, and over-saturated generations. In light of the above issues, we present Consist3D, a three-stage framework Chasing for semantic-, geometric-, and saturation-Consistent Text-to-3D generation from a single image, in which the first two stages aim to learn parameterized consistency tokens, and the last stage is for optimization. Specifically, the semantic encoding stage learns a token independent of views and estimations, promoting semantic consistency and robustness. Meanwhile, the geometric encoding stage learns another token with comprehensive geometry and reconstruction constraints under novel-view estimations, reducing overfitting and encouraging geometric consistency. Finally, the optimization stage benefits from the semantic and geometric tokens, allowing a low classifier-free guidance scale and therefore preventing oversaturation. Experimental results demonstrate that Consist3D produces more consistent, faithful, and photo-realistic 3D assets compared to previous state-of-the-art methods. Furthermore, Consist3D also allows background and object editing through text prompts.

Advancements in 3D Gaussian Splatting have significantly accelerated 3D reconstruction and generation. However, it may require a large number of Gaussians, which creates a substantial memory footprint. This paper introduces GES (Generalized Exponential Splatting), a novel representation that employs Generalized Exponential Function (GEF) to model 3D scenes, requiring far fewer particles to represent a scene and thus significantly outperforming Gaussian Splatting methods in efficiency with a plug-and-play replacement ability for Gaussian-based utilities. GES is validated theoretically and empirically in both principled 1D setup and realistic 3D scenes. It is shown to represent signals with sharp edges more accurately, which are typically challenging for Gaussians due to their inherent low-pass characteristics. Our empirical analysis demonstrates that GEF outperforms Gaussians in fitting natural-occurring signals (e.g. squares, triangles, and parabolic signals), thereby reducing the need for extensive splitting operations that increase the memory footprint of Gaussian Splatting. With the aid of a frequency-modulated loss, GES achieves competitive performance in novel-view synthesis benchmarks while requiring less than half the memory storage of Gaussian Splatting and increasing the rendering speed by up to 39%. The code is available on the project website https://abdullahamdi.com/ges .

Constructing photo-realistic Free-Viewpoint Videos (FVVs) of dynamic scenes from multi-view videos remains a challenging endeavor. Despite the remarkable advancements achieved by current neural rendering techniques, these methods generally require complete video sequences for offline training and are not capable of real-time rendering. To address these constraints, we introduce 3DGStream, a method designed for efficient FVV streaming of real-world dynamic scenes. Our method achieves fast on-the-fly per-frame reconstruction within 12 seconds and real-time rendering at 200 FPS. Specifically, we utilize 3D Gaussians (3DGs) to represent the scene. Instead of the na\"ive approach of directly optimizing 3DGs per-frame, we employ a compact Neural Transformation Cache (NTC) to model the translations and rotations of 3DGs, markedly reducing the training time and storage required for each FVV frame. Furthermore, we propose an adaptive 3DG addition strategy to handle emerging objects in dynamic scenes. Experiments demonstrate that 3DGStream achieves competitive performance in terms of rendering speed, image quality, training time, and model storage when compared with state-of-the-art methods.

Depth maps are widely used in feed-forward 3D Gaussian Splatting (3DGS) pipelines by unprojecting them into 3D point clouds for novel view synthesis. This approach offers advantages such as efficient training, the use of known camera poses, and accurate geometry estimation. However, depth discontinuities at object boundaries often lead to fragmented or sparse point clouds, degrading rendering quality -- a well-known limitation of depth-based representations. To tackle this issue, we introduce PM-Loss, a novel regularization loss based on a pointmap predicted by a pre-trained transformer. Although the pointmap itself may be less accurate than the depth map, it effectively enforces geometric smoothness, especially around object boundaries. With the improved depth map, our method significantly improves the feed-forward 3DGS across various architectures and scenes, delivering consistently better rendering results. Our project page: https://aim-uofa.github.io/PMLoss

Recent facial image synthesis methods have been mainly based on conditional generative models. Sketch-based conditions can effectively describe the geometry of faces, including the contours of facial components, hair structures, as well as salient edges (e.g., wrinkles) on face surfaces but lack effective control of appearance, which is influenced by color, material, lighting condition, etc. To have more control of generated results, one possible approach is to apply existing disentangling works to disentangle face images into geometry and appearance representations. However, existing disentangling methods are not optimized for human face editing, and cannot achieve fine control of facial details such as wrinkles. To address this issue, we propose DeepFaceEditing, a structured disentanglement framework specifically designed for face images to support face generation and editing with disentangled control of geometry and appearance. We adopt a local-to-global approach to incorporate the face domain knowledge: local component images are decomposed into geometry and appearance representations, which are fused consistently using a global fusion module to improve generation quality. We exploit sketches to assist in extracting a better geometry representation, which also supports intuitive geometry editing via sketching. The resulting method can either extract the geometry and appearance representations from face images, or directly extract the geometry representation from face sketches. Such representations allow users to easily edit and synthesize face images, with decoupled control of their geometry and appearance. Both qualitative and quantitative evaluations show the superior detail and appearance control abilities of our method compared to state-of-the-art methods.

We present a learning-based method, namely GeoUDF,to tackle the long-standing and challenging problem of reconstructing a discrete surface from a sparse point cloud.To be specific, we propose a geometry-guided learning method for UDF and its gradient estimation that explicitly formulates the unsigned distance of a query point as the learnable affine averaging of its distances to the tangent planes of neighboring points on the surface. Besides,we model the local geometric structure of the input point clouds by explicitly learning a quadratic polynomial for each point. This not only facilitates upsampling the input sparse point cloud but also naturally induces unoriented normal, which further augments UDF estimation. Finally, to extract triangle meshes from the predicted UDF we propose a customized edge-based marching cube module. We conduct extensive experiments and ablation studies to demonstrate the significant advantages of our method over state-of-the-art methods in terms of reconstruction accuracy, efficiency, and generality. The source code is publicly available at https://github.com/rsy6318/GeoUDF.

Recovery of an underlying scene geometry from multiview images stands as a long-time challenge in computer vision research. The recent promise leverages neural implicit surface learning and differentiable volume rendering, and achieves both the recovery of scene geometry and synthesis of novel views, where deep priors of neural models are used as an inductive smoothness bias. While promising for object-level surfaces, these methods suffer when coping with complex scene surfaces. In the meanwhile, traditional multi-view stereo can recover the geometry of scenes with rich textures, by globally optimizing the local, pixel-wise correspondences across multiple views. We are thus motivated to make use of the complementary benefits from the two strategies, and propose a method termed Helix-shaped neural implicit Surface learning or HelixSurf; HelixSurf uses the intermediate prediction from one strategy as the guidance to regularize the learning of the other one, and conducts such intertwined regularization iteratively during the learning process. We also propose an efficient scheme for differentiable volume rendering in HelixSurf. Experiments on surface reconstruction of indoor scenes show that our method compares favorably with existing methods and is orders of magnitude faster, even when some of existing methods are assisted with auxiliary training data. The source code is available at https://github.com/Gorilla-Lab-SCUT/HelixSurf.

3D vector graphics play a crucial role in various applications including 3D shape retrieval, conceptual design, and virtual reality interactions due to their ability to capture essential structural information with minimal representation. While recent approaches have shown promise in generating 3D vector graphics, they often suffer from lengthy processing times and struggle to maintain view consistency. To address these limitations, we propose ViewCraft3D (VC3D), an efficient method that leverages 3D priors to generate 3D vector graphics. Specifically, our approach begins with 3D object analysis, employs a geometric extraction algorithm to fit 3D vector graphics to the underlying structure, and applies view-consistent refinement process to enhance visual quality. Our comprehensive experiments demonstrate that VC3D outperforms previous methods in both qualitative and quantitative evaluations, while significantly reducing computational overhead. The resulting 3D sketches maintain view consistency and effectively capture the essential characteristics of the original objects.

Neural surface representation has demonstrated remarkable success in the areas of novel view synthesis and 3D reconstruction. However, assessing the geometric quality of 3D reconstructions in the absence of ground truth mesh remains a significant challenge, due to its rendering-based optimization process and entangled learning of appearance and geometry with photometric losses. In this paper, we present a novel framework, i.e, GURecon, which establishes a geometric uncertainty field for the neural surface based on geometric consistency. Different from existing methods that rely on rendering-based measurement, GURecon models a continuous 3D uncertainty field for the reconstructed surface, and is learned by an online distillation approach without introducing real geometric information for supervision. Moreover, in order to mitigate the interference of illumination on geometric consistency, a decoupled field is learned and exploited to finetune the uncertainty field. Experiments on various datasets demonstrate the superiority of GURecon in modeling 3D geometric uncertainty, as well as its plug-and-play extension to various neural surface representations and improvement on downstream tasks such as incremental reconstruction. The code and supplementary material are available on the project website: https://zju3dv.github.io/GURecon/.

3D AI-generated content (AIGC) has made it increasingly accessible for anyone to become a 3D content creator. While recent methods leverage Score Distillation Sampling to distill 3D objects from pretrained image diffusion models, they often suffer from inadequate 3D priors, leading to insufficient multi-view consistency. In this work, we introduce NOVA3D, an innovative single-image-to-3D generation framework. Our key insight lies in leveraging strong 3D priors from a pretrained video diffusion model and integrating geometric information during multi-view video fine-tuning. To facilitate information exchange between color and geometric domains, we propose the Geometry-Temporal Alignment (GTA) attention mechanism, thereby improving generalization and multi-view consistency. Moreover, we introduce the de-conflict geometry fusion algorithm, which improves texture fidelity by addressing multi-view inaccuracies and resolving discrepancies in pose alignment. Extensive experiments validate the superiority of NOVA3D over existing baselines.

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

Presenting a 3D scene from multiview images remains a core and long-standing challenge in computer vision and computer graphics. Two main requirements lie in rendering and reconstruction. Notably, SOTA rendering quality is usually achieved with neural volumetric rendering techniques, which rely on aggregated point/primitive-wise color and neglect the underlying scene geometry. Learning of neural implicit surfaces is sparked from the success of neural rendering. Current works either constrain the distribution of density fields or the shape of primitives, resulting in degraded rendering quality and flaws on the learned scene surfaces. The efficacy of such methods is limited by the inherent constraints of the chosen neural representation, which struggles to capture fine surface details, especially for larger, more intricate scenes. To address these issues, we introduce GSDF, a novel dual-branch architecture that combines the benefits of a flexible and efficient 3D Gaussian Splatting (3DGS) representation with neural Signed Distance Fields (SDF). The core idea is to leverage and enhance the strengths of each branch while alleviating their limitation through mutual guidance and joint supervision. We show on diverse scenes that our design unlocks the potential for more accurate and detailed surface reconstructions, and at the meantime benefits 3DGS rendering with structures that are more aligned with the underlying geometry.

In this paper, we democratise 3D content creation, enabling precise generation of 3D shapes from abstract sketches while overcoming limitations tied to drawing skills. We introduce a novel part-level modelling and alignment framework that facilitates abstraction modelling and cross-modal correspondence. Leveraging the same part-level decoder, our approach seamlessly extends to sketch modelling by establishing correspondence between CLIPasso edgemaps and projected 3D part regions, eliminating the need for a dataset pairing human sketches and 3D shapes. Additionally, our method introduces a seamless in-position editing process as a byproduct of cross-modal part-aligned modelling. Operating in a low-dimensional implicit space, our approach significantly reduces computational demands and processing time.

Remarkable advances have been achieved recently in learning neural representations that characterize object geometry, while generating textured objects suitable for downstream applications and 3D rendering remains at an early stage. In particular, reconstructing textured geometry from images of real objects is a significant challenge -- reconstructed geometry is often inexact, making realistic texturing a significant challenge. We present Mesh2Tex, which learns a realistic object texture manifold from uncorrelated collections of 3D object geometry and photorealistic RGB images, by leveraging a hybrid mesh-neural-field texture representation. Our texture representation enables compact encoding of high-resolution textures as a neural field in the barycentric coordinate system of the mesh faces. The learned texture manifold enables effective navigation to generate an object texture for a given 3D object geometry that matches to an input RGB image, which maintains robustness even under challenging real-world scenarios where the mesh geometry approximates an inexact match to the underlying geometry in the RGB image. Mesh2Tex can effectively generate realistic object textures for an object mesh to match real images observations towards digitization of real environments, significantly improving over previous state of the art.

We introduce a diffusion-based framework that performs aligned novel view image and geometry generation via a warping-and-inpainting methodology. Unlike prior methods that require dense posed images or pose-embedded generative models limited to in-domain views, our method leverages off-the-shelf geometry predictors to predict partial geometries viewed from reference images, and formulates novel-view synthesis as an inpainting task for both image and geometry. To ensure accurate alignment between generated images and geometry, we propose cross-modal attention distillation, where attention maps from the image diffusion branch are injected into a parallel geometry diffusion branch during both training and inference. This multi-task approach achieves synergistic effects, facilitating geometrically robust image synthesis as well as well-defined geometry prediction. We further introduce proximity-based mesh conditioning to integrate depth and normal cues, interpolating between point cloud and filtering erroneously predicted geometry from influencing the generation process. Empirically, our method achieves high-fidelity extrapolative view synthesis on both image and geometry across a range of unseen scenes, delivers competitive reconstruction quality under interpolation settings, and produces geometrically aligned colored point clouds for comprehensive 3D completion. Project page is available at https://cvlab-kaist.github.io/MoAI.

The popularity of pre-trained large models has revolutionized downstream tasks across diverse fields, such as language, vision, and multi-modality. To minimize the adaption cost for downstream tasks, many Parameter-Efficient Fine-Tuning (PEFT) techniques are proposed for language and 2D image pre-trained models. However, the specialized PEFT method for 3D pre-trained models is still under-explored. To this end, we introduce Point-PEFT, a novel framework for adapting point cloud pre-trained models with minimal learnable parameters. Specifically, for a pre-trained 3D model, we freeze most of its parameters, and only tune the newly added PEFT modules on downstream tasks, which consist of a Point-prior Prompt and a Geometry-aware Adapter. The Point-prior Prompt adopts a set of learnable prompt tokens, for which we propose to construct a memory bank with domain-specific knowledge, and utilize a parameter-free attention to enhance the prompt tokens. The Geometry-aware Adapter aims to aggregate point cloud features within spatial neighborhoods to capture fine-grained geometric information through local interactions. Extensive experiments indicate that our Point-PEFT can achieve better performance than the full fine-tuning on various downstream tasks, while using only 5% of the trainable parameters, demonstrating the efficiency and effectiveness of our approach. Code is released at https://github.com/Ivan-Tang-3D/Point-PEFT.

In recent years, 3D Gaussian splatting has emerged as a powerful technique for 3D reconstruction and generation, known for its fast and high-quality rendering capabilities. To address these shortcomings, this paper introduces a novel diffusion-based framework, GVGEN, designed to efficiently generate 3D Gaussian representations from text input. We propose two innovative techniques:(1) Structured Volumetric Representation. We first arrange disorganized 3D Gaussian points as a structured form GaussianVolume. This transformation allows the capture of intricate texture details within a volume composed of a fixed number of Gaussians. To better optimize the representation of these details, we propose a unique pruning and densifying method named the Candidate Pool Strategy, enhancing detail fidelity through selective optimization. (2) Coarse-to-fine Generation Pipeline. To simplify the generation of GaussianVolume and empower the model to generate instances with detailed 3D geometry, we propose a coarse-to-fine pipeline. It initially constructs a basic geometric structure, followed by the prediction of complete Gaussian attributes. Our framework, GVGEN, demonstrates superior performance in qualitative and quantitative assessments compared to existing 3D generation methods. Simultaneously, it maintains a fast generation speed (sim7 seconds), effectively striking a balance between quality and efficiency.

Compositionality, the notion that the meaning of an expression is constructed from the meaning of its parts and syntactic rules, permits the infinite productivity of human language. For the first time, artificial language models (LMs) are able to match human performance in a number of compositional generalization tasks. However, much remains to be understood about the representational mechanisms underlying these abilities. We take a high-level geometric approach to this problem by relating the degree of compositionality in a dataset to the intrinsic dimensionality of its representations under an LM, a measure of feature complexity. We find not only that the degree of dataset compositionality is reflected in representations' intrinsic dimensionality, but that the relationship between compositionality and geometric complexity arises due to learned linguistic features over training. Finally, our analyses reveal a striking contrast between linear and nonlinear dimensionality, showing that they respectively encode formal and semantic aspects of linguistic composition.

Diffusion models for single image novel view synthesis (NVS) can generate highly realistic and plausible images, but they are limited in the geometric consistency to the given relative poses. The generated images often show significant errors with respect to the epipolar constraints that should be fulfilled, as given by the target pose. In this paper we address this issue by proposing a methodology to improve the geometric correctness of images generated by a diffusion model for single image NVS. We formulate a loss function based on image matching and epipolar constraints, and optimize the starting noise in a diffusion sampling process such that the generated image should both be a realistic image and fulfill geometric constraints derived from the given target pose. Our method does not require training data or fine-tuning of the diffusion models, and we show that we can apply it to multiple state-of-the-art models for single image NVS. The method is evaluated on the MegaScenes dataset and we show that geometric consistency is improved compared to the baseline models while retaining the quality of the generated images.

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus on optimizing local updates or global aggregation, but these indirect approaches demonstrate instability when handling highly heterogeneous data distributions, especially in scenarios where label skew and domain skew coexist. To address this, we propose a geometry-guided data generation method that centers on simulating the global embedding distribution locally. We first introduce the concept of the geometric shape of an embedding distribution and then address the challenge of obtaining global geometric shapes under privacy constraints. Subsequently, we propose GGEUR, which leverages global geometric shapes to guide the generation of new samples, enabling a closer approximation to the ideal global distribution. In single-domain scenarios, we augment samples based on global geometric shapes to enhance model generalization; in multi-domain scenarios, we further employ class prototypes to simulate the global distribution across domains. Extensive experimental results demonstrate that our method significantly enhances the performance of existing approaches in handling highly heterogeneous data, including scenarios with label skew, domain skew, and their coexistence. Code published at: https://github.com/WeiDai-David/2025CVPR_GGEUR

3D cellular image segmentation methods are commonly divided into non-2D-based and 2D-based approaches, the latter reconstructing 3D shapes from the segmentation results of 2D layers. However, errors in 2D results often propagate, leading to oversegmentations in the final 3D results. To tackle this issue, we introduce an interpretable geometric framework that addresses the oversegmentations by correcting the 2D segmentation results based on geometric information from adjacent layers. Leveraging both geometric (layer-to-layer, 2D) and topological (3D shape) features, we use binary classification to determine whether neighboring cells should be stitched. We develop a pre-trained classifier on public plant cell datasets and validate its performance on animal cell datasets, confirming its effectiveness in correcting oversegmentations under the transfer learning setting. Furthermore, we demonstrate that our framework can be extended to correcting oversegmentation on non-2D-based methods. A clear pipeline is provided for end-users to build the pre-trained model to any labeled dataset.

Geometric ability is a significant challenge for large language models (LLMs) due to the need for advanced spatial comprehension and abstract thinking. Existing datasets primarily evaluate LLMs on their final answers, but they cannot truly measure their true understanding of geometric structures, as LLMs can arrive at correct answers by coincidence. To fill this gap, we introduce the GeomRel dataset, designed to evaluate LLMs' understanding of geometric structures by isolating the core step of geometric relationship identification in problem-solving. Using this benchmark, we conduct thorough evaluations of diverse LLMs and identify key limitations in understanding geometric structures. We further propose the Geometry Chain-of-Thought (GeoCoT) method, which enhances LLMs' ability to identify geometric relationships, resulting in significant performance improvements.

Multimodal large language models (MLLMs) have made significant progress in integrating visual and linguistic understanding. Existing benchmarks typically focus on high-level semantic capabilities, such as scene understanding and visual reasoning, but often overlook a crucial, foundational ability: geometric perception. Geometric perception involves understanding geometric shapes, structures, and spatial relationships, which are essential for supporting higher-level semantic tasks. Despite its importance, this capability remains underexplored in current MLLM research. To address this gap, we introduce GePBench, a novel benchmark designed to assess the geometric perception abilities of MLLMs. Our extensive evaluations reveal that current state-of-the-art MLLMs exhibit significant deficiencies in geometric perception tasks. Furthermore, we show that models trained with GePBench data demonstrate substantial improvements on a wide range of benchmark tasks, highlighting the critical role of geometric perception in enabling advanced multimodal applications. Our code and datasets will be publicly available.

Denoising diffusion models have shown great potential in multiple research areas. Existing diffusion-based generative methods on de novo 3D molecule generation face two major challenges. Since majority heavy atoms in molecules allow connections to multiple atoms through single bonds, solely using pair-wise distance to model molecule geometries is insufficient. Therefore, the first one involves proposing an effective neural network as the denoising kernel that is capable to capture complex multi-body interatomic relationships and learn high-quality features. Due to the discrete nature of graphs, mainstream diffusion-based methods for molecules heavily rely on predefined rules and generate edges in an indirect manner. The second challenge involves accommodating molecule generation to diffusion and accurately predicting the existence of bonds. In our research, we view the iterative way of updating molecule conformations in diffusion process is consistent with molecular dynamics and introduce a novel molecule generation method named Geometric-Facilitated Molecular Diffusion (GFMDiff). For the first challenge, we introduce a Dual-Track Transformer Network (DTN) to fully excevate global spatial relationships and learn high quality representations which contribute to accurate predictions of features and geometries. As for the second challenge, we design Geometric-Facilitated Loss (GFLoss) which intervenes the formation of bonds during the training period, instead of directly embedding edges into the latent space. Comprehensive experiments on current benchmarks demonstrate the superiority of GFMDiff.

We present the wakefield conformal mapping technique that can be readily applied to the analysis of the radiation generated by an ultra-relativistic particle in the step transition and a collimator. We derive simple analytical expressions for the lower and upper bounds of both longitudinal and transverse wake potentials. We test the derived expressions against well-known formulas in several representative examples. The proposed method can greatly simplify the optimization of collimating sections, as well as become a useful tool in the shape optimization problems.

Generative models, especially diffusion models (DMs), have achieved promising results for generating feature-rich geometries and advancing foundational science problems such as molecule design. Inspired by the recent huge success of Stable (latent) Diffusion models, we propose a novel and principled method for 3D molecule generation named Geometric Latent Diffusion Models (GeoLDM). GeoLDM is the first latent DM model for the molecular geometry domain, composed of autoencoders encoding structures into continuous latent codes and DMs operating in the latent space. Our key innovation is that for modeling the 3D molecular geometries, we capture its critical roto-translational equivariance constraints by building a point-structured latent space with both invariant scalars and equivariant tensors. Extensive experiments demonstrate that GeoLDM can consistently achieve better performance on multiple molecule generation benchmarks, with up to 7\% improvement for the valid percentage of large biomolecules. Results also demonstrate GeoLDM's higher capacity for controllable generation thanks to the latent modeling. Code is provided at https://github.com/MinkaiXu/GeoLDM.

Multi-camera 3D object detection for autonomous driving is a challenging problem that has garnered notable attention from both academia and industry. An obstacle encountered in vision-based techniques involves the precise extraction of geometry-conscious features from RGB images. Recent approaches have utilized geometric-aware image backbones pretrained on depth-relevant tasks to acquire spatial information. However, these approaches overlook the critical aspect of view transformation, resulting in inadequate performance due to the misalignment of spatial knowledge between the image backbone and view transformation. To address this issue, we propose a novel geometric-aware pretraining framework called GAPretrain. Our approach incorporates spatial and structural cues to camera networks by employing the geometric-rich modality as guidance during the pretraining phase. The transference of modal-specific attributes across different modalities is non-trivial, but we bridge this gap by using a unified bird's-eye-view (BEV) representation and structural hints derived from LiDAR point clouds to facilitate the pretraining process. GAPretrain serves as a plug-and-play solution that can be flexibly applied to multiple state-of-the-art detectors. Our experiments demonstrate the effectiveness and generalization ability of the proposed method. We achieve 46.2 mAP and 55.5 NDS on the nuScenes val set using the BEVFormer method, with a gain of 2.7 and 2.1 points, respectively. We also conduct experiments on various image backbones and view transformations to validate the efficacy of our approach. Code will be released at https://github.com/OpenDriveLab/BEVPerception-Survey-Recipe.

The two-stage object pose estimation paradigm first detects semantic keypoints on the image and then estimates the 6D pose by minimizing reprojection errors. Despite performing well on standard benchmarks, existing techniques offer no provable guarantees on the quality and uncertainty of the estimation. In this paper, we inject two fundamental changes, namely conformal keypoint detection and geometric uncertainty propagation, into the two-stage paradigm and propose the first pose estimator that endows an estimation with provable and computable worst-case error bounds. On one hand, conformal keypoint detection applies the statistical machinery of inductive conformal prediction to convert heuristic keypoint detections into circular or elliptical prediction sets that cover the groundtruth keypoints with a user-specified marginal probability (e.g., 90%). Geometric uncertainty propagation, on the other, propagates the geometric constraints on the keypoints to the 6D object pose, leading to a Pose UnceRtainty SEt (PURSE) that guarantees coverage of the groundtruth pose with the same probability. The PURSE, however, is a nonconvex set that does not directly lead to estimated poses and uncertainties. Therefore, we develop RANdom SAmple averaGing (RANSAG) to compute an average pose and apply semidefinite relaxation to upper bound the worst-case errors between the average pose and the groundtruth. On the LineMOD Occlusion dataset we demonstrate: (i) the PURSE covers the groundtruth with valid probabilities; (ii) the worst-case error bounds provide correct uncertainty quantification; and (iii) the average pose achieves better or similar accuracy as representative methods based on sparse keypoints.

Geometric methods for solving open-world off-road navigation tasks, by learning occupancy and metric maps, provide good generalization but can be brittle in outdoor environments that violate their assumptions (e.g., tall grass). Learning-based methods can directly learn collision-free behavior from raw observations, but are difficult to integrate with standard geometry-based pipelines. This creates an unfortunate conflict -- either use learning and lose out on well-understood geometric navigational components, or do not use it, in favor of extensively hand-tuned geometry-based cost maps. In this work, we reject this dichotomy by designing the learning and non-learning-based components in a way such that they can be effectively combined in a self-supervised manner. Both components contribute to a planning criterion: the learned component contributes predicted traversability as rewards, while the geometric component contributes obstacle cost information. We instantiate and comparatively evaluate our system in both in-distribution and out-of-distribution environments, showing that this approach inherits complementary gains from the learned and geometric components and significantly outperforms either of them. Videos of our results are hosted at https://sites.google.com/view/hybrid-imitative-planning

Geometric alignment appears in a variety of applications, ranging from domain adaptation, optimal transport, and normalizing flows in machine learning; optical flow and learned augmentation in computer vision and deformable registration within biomedical imaging. A recurring challenge is the alignment of domains whose topology is not the same; a problem that is routinely ignored, potentially introducing bias in downstream analysis. As a first step towards solving such alignment problems, we propose an unsupervised algorithm for the detection of changes in image topology. The model is based on a conditional variational auto-encoder and detects topological changes between two images during the registration step. We account for both topological changes in the image under spatial variation and unexpected transformations. Our approach is validated on two tasks and datasets: detection of topological changes in microscopy images of cells, and unsupervised anomaly detection brain imaging.

In this paper, we propose Img2CAD, the first approach to our knowledge that uses 2D image inputs to generate CAD models with editable parameters. Unlike existing AI methods for 3D model generation using text or image inputs often rely on mesh-based representations, which are incompatible with CAD tools and lack editability and fine control, Img2CAD enables seamless integration between AI-based 3D reconstruction and CAD software. We have identified an innovative intermediate representation called Structured Visual Geometry (SVG), characterized by vectorized wireframes extracted from objects. This representation significantly enhances the performance of generating conditioned CAD models. Additionally, we introduce two new datasets to further support research in this area: ABC-mono, the largest known dataset comprising over 200,000 3D CAD models with rendered images, and KOCAD, the first dataset featuring real-world captured objects alongside their ground truth CAD models, supporting further research in conditioned CAD model generation.

Polygon meshes are an efficient representation of 3D geometry, and are of central importance in computer graphics, robotics and games development. Existing learning-based approaches have avoided the challenges of working with 3D meshes, instead using alternative object representations that are more compatible with neural architectures and training approaches. We present an approach which models the mesh directly, predicting mesh vertices and faces sequentially using a Transformer-based architecture. Our model can condition on a range of inputs, including object classes, voxels, and images, and because the model is probabilistic it can produce samples that capture uncertainty in ambiguous scenarios. We show that the model is capable of producing high-quality, usable meshes, and establish log-likelihood benchmarks for the mesh-modelling task. We also evaluate the conditional models on surface reconstruction metrics against alternative methods, and demonstrate competitive performance despite not training directly on this task.

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently unable to scale to high dimensions, or use approximations for limiting quantities that result in biased training objectives. Riemannian Flow Matching bypasses these limitations and offers several advantages over previous approaches: it is simulation-free on simple geometries, does not require divergence computation, and computes its target vector field in closed-form. The key ingredient behind RFM is the construction of a relatively simple premetric for defining target vector fields, which encompasses the existing Euclidean case. To extend to general geometries, we rely on the use of spectral decompositions to efficiently compute premetrics on the fly. Our method achieves state-of-the-art performance on many real-world non-Euclidean datasets, and we demonstrate tractable training on general geometries, including triangular meshes with highly non-trivial curvature and boundaries.

To address the data scarcity associated with 3D assets, 2D-lifting techniques such as Score Distillation Sampling (SDS) have become a widely adopted practice in text-to-3D generation pipelines. However, the diffusion models used in these techniques are prone to viewpoint bias and thus lead to geometric inconsistencies such as the Janus problem. To counter this, we introduce MT3D, a text-to-3D generative model that leverages a high-fidelity 3D object to overcome viewpoint bias and explicitly infuse geometric understanding into the generation pipeline. Firstly, we employ depth maps derived from a high-quality 3D model as control signals to guarantee that the generated 2D images preserve the fundamental shape and structure, thereby reducing the inherent viewpoint bias. Next, we utilize deep geometric moments to ensure geometric consistency in the 3D representation explicitly. By incorporating geometric details from a 3D asset, MT3D enables the creation of diverse and geometrically consistent objects, thereby improving the quality and usability of our 3D representations.

We introduce CLR-Wire, a novel framework for 3D curve-based wireframe generation that integrates geometry and topology into a unified Continuous Latent Representation. Unlike conventional methods that decouple vertices, edges, and faces, CLR-Wire encodes curves as Neural Parametric Curves along with their topological connectivity into a continuous and fixed-length latent space using an attention-driven variational autoencoder (VAE). This unified approach facilitates joint learning and generation of both geometry and topology. To generate wireframes, we employ a flow matching model to progressively map Gaussian noise to these latents, which are subsequently decoded into complete 3D wireframes. Our method provides fine-grained modeling of complex shapes and irregular topologies, and supports both unconditional generation and generation conditioned on point cloud or image inputs. Experimental results demonstrate that, compared with state-of-the-art generative approaches, our method achieves substantial improvements in accuracy, novelty, and diversity, offering an efficient and comprehensive solution for CAD design, geometric reconstruction, and 3D content creation.

Feed-forward 3D generative models like the Large Reconstruction Model (LRM) have demonstrated exceptional generation speed. However, the transformer-based methods do not leverage the geometric priors of the triplane component in their architecture, often leading to sub-optimal quality given the limited size of 3D data and slow training. In this work, we present the Convolutional Reconstruction Model (CRM), a high-fidelity feed-forward single image-to-3D generative model. Recognizing the limitations posed by sparse 3D data, we highlight the necessity of integrating geometric priors into network design. CRM builds on the key observation that the visualization of triplane exhibits spatial correspondence of six orthographic images. First, it generates six orthographic view images from a single input image, then feeds these images into a convolutional U-Net, leveraging its strong pixel-level alignment capabilities and significant bandwidth to create a high-resolution triplane. CRM further employs Flexicubes as geometric representation, facilitating direct end-to-end optimization on textured meshes. Overall, our model delivers a high-fidelity textured mesh from an image in just 10 seconds, without any test-time optimization.

In this paper, we introduce MeshGen, an advanced image-to-3D pipeline that generates high-quality 3D meshes with detailed geometry and physically based rendering (PBR) textures. Addressing the challenges faced by existing 3D native diffusion models, such as suboptimal auto-encoder performance, limited controllability, poor generalization, and inconsistent image-based PBR texturing, MeshGen employs several key innovations to overcome these limitations. We pioneer a render-enhanced point-to-shape auto-encoder that compresses meshes into a compact latent space by designing perceptual optimization with ray-based regularization. This ensures that the 3D shapes are accurately represented and reconstructed to preserve geometric details within the latent space. To address data scarcity and image-shape misalignment, we further propose geometric augmentation and generative rendering augmentation techniques, which enhance the model's controllability and generalization ability, allowing it to perform well even with limited public datasets. For the texture generation, MeshGen employs a reference attention-based multi-view ControlNet for consistent appearance synthesis. This is further complemented by our multi-view PBR decomposer that estimates PBR components and a UV inpainter that fills invisible areas, ensuring a seamless and consistent texture across the 3D mesh. Our extensive experiments demonstrate that MeshGen largely outperforms previous methods in both shape and texture generation, setting a new standard for the quality of 3D meshes generated with PBR textures. See our code at https://github.com/heheyas/MeshGen, project page https://heheyas.github.io/MeshGen

Using parts of existing models to rebuild new models, commonly termed as example-based modeling, is a classical methodology in the realm of computer graphics. Previous works mostly focus on shape composition, making them very hard to use for realistic composition of 3D objects captured from real-world scenes. This leads to combining multiple NeRFs into a single 3D scene to achieve seamless appearance blending. However, the current SeamlessNeRF method struggles to achieve interactive editing and harmonious stitching for real-world scenes due to its gradient-based strategy and grid-based representation. To this end, we present an example-based modeling method that combines multiple Gaussian fields in a point-based representation using sample-guided synthesis. Specifically, as for composition, we create a GUI to segment and transform multiple fields in real time, easily obtaining a semantically meaningful composition of models represented by 3D Gaussian Splatting (3DGS). For texture blending, due to the discrete and irregular nature of 3DGS, straightforwardly applying gradient propagation as SeamlssNeRF is not supported. Thus, a novel sampling-based cloning method is proposed to harmonize the blending while preserving the original rich texture and content. Our workflow consists of three steps: 1) real-time segmentation and transformation of a Gaussian model using a well-tailored GUI, 2) KNN analysis to identify boundary points in the intersecting area between the source and target models, and 3) two-phase optimization of the target model using sampling-based cloning and gradient constraints. Extensive experimental results validate that our approach significantly outperforms previous works in terms of realistic synthesis, demonstrating its practicality. More demos are available at https://ingra14m.github.io/gs_stitching_website.

Recent advances in diffusion models have demonstrated exceptional capabilities in image and video generation, further improving the effectiveness of 4D synthesis. Existing 4D generation methods can generate high-quality 4D objects or scenes based on user-friendly conditions, benefiting the gaming and video industries. However, these methods struggle to synthesize significant object deformation of complex 4D transitions and interactions within scenes. To address this challenge, we propose Trans4D, a novel text-to-4D synthesis framework that enables realistic complex scene transitions. Specifically, we first use multi-modal large language models (MLLMs) to produce a physic-aware scene description for 4D scene initialization and effective transition timing planning. Then we propose a geometry-aware 4D transition network to realize a complex scene-level 4D transition based on the plan, which involves expressive geometrical object deformation. Extensive experiments demonstrate that Trans4D consistently outperforms existing state-of-the-art methods in generating 4D scenes with accurate and high-quality transitions, validating its effectiveness. Code: https://github.com/YangLing0818/Trans4D

3D scene generation conditioned on text prompts has significantly progressed due to the development of 2D diffusion generation models. However, the textual description of 3D scenes is inherently inaccurate and lacks fine-grained control during training, leading to implausible scene generation. As an intuitive and feasible solution, the 3D layout allows for precise specification of object locations within the scene. To this end, we present a text-to-scene generation method (namely, Layout2Scene) using additional semantic layout as the prompt to inject precise control of 3D object positions. Specifically, we first introduce a scene hybrid representation to decouple objects and backgrounds, which is initialized via a pre-trained text-to-3D model. Then, we propose a two-stage scheme to optimize the geometry and appearance of the initialized scene separately. To fully leverage 2D diffusion priors in geometry and appearance generation, we introduce a semantic-guided geometry diffusion model and a semantic-geometry guided diffusion model which are finetuned on a scene dataset. Extensive experiments demonstrate that our method can generate more plausible and realistic scenes as compared to state-of-the-art approaches. Furthermore, the generated scene allows for flexible yet precise editing, thereby facilitating multiple downstream applications.

The integration of geometric reconstruction and generative modeling remains a critical challenge in developing AI systems capable of human-like spatial reasoning. This paper proposes Aether, a unified framework that enables geometry-aware reasoning in world models by jointly optimizing three core capabilities: (1) 4D dynamic reconstruction, (2) action-conditioned video prediction, and (3) goal-conditioned visual planning. Through task-interleaved feature learning, Aether achieves synergistic knowledge sharing across reconstruction, prediction, and planning objectives. Building upon video generation models, our framework demonstrates unprecedented synthetic-to-real generalization despite never observing real-world data during training. Furthermore, our approach achieves zero-shot generalization in both action following and reconstruction tasks, thanks to its intrinsic geometric modeling. Remarkably, even without real-world data, its reconstruction performance far exceeds that of domain-specific models. Additionally, Aether leverages a geometry-informed action space to seamlessly translate predictions into actions, enabling effective autonomous trajectory planning. We hope our work inspires the community to explore new frontiers in physically-reasonable world modeling and its applications.

Mathematical geometric problem solving (GPS) often requires effective integration of multimodal information and verifiable logical coherence. Despite the fast development of large language models in general problem solving, it remains unresolved regarding with both methodology and benchmarks, especially given the fact that exiting synthetic GPS benchmarks are often not self-verified and contain noise and self-contradicted information due to the illusion of LLMs. In this paper, we propose a scalable data engine called TrustGeoGen for problem generation, with formal verification to provide a principled benchmark, which we believe lays the foundation for the further development of methods for GPS. The engine synthesizes geometric data through four key innovations: 1) multimodal-aligned generation of diagrams, textual descriptions, and stepwise solutions; 2) formal verification ensuring rule-compliant reasoning paths; 3) a bootstrapping mechanism enabling complexity escalation via recursive state generation and 4) our devised GeoExplore series algorithms simultaneously produce multi-solution variants and self-reflective backtracking traces. By formal logical verification, TrustGeoGen produces GeoTrust-200K dataset with guaranteed modality integrity, along with GeoTrust-test testset. Experiments reveal the state-of-the-art models achieve only 49.17\% accuracy on GeoTrust-test, demonstrating its evaluation stringency. Crucially, models trained on GeoTrust achieve OOD generalization on GeoQA, significantly reducing logical inconsistencies relative to pseudo-label annotated by OpenAI-o1. Our code is available at https://github.com/Alpha-Innovator/TrustGeoGen

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k.

Multi-view stereo reconstruction (MVS) in the wild requires to first estimate the camera parameters e.g. intrinsic and extrinsic parameters. These are usually tedious and cumbersome to obtain, yet they are mandatory to triangulate corresponding pixels in 3D space, which is the core of all best performing MVS algorithms. In this work, we take an opposite stance and introduce DUSt3R, a radically novel paradigm for Dense and Unconstrained Stereo 3D Reconstruction of arbitrary image collections, i.e. operating without prior information about camera calibration nor viewpoint poses. We cast the pairwise reconstruction problem as a regression of pointmaps, relaxing the hard constraints of usual projective camera models. We show that this formulation smoothly unifies the monocular and binocular reconstruction cases. In the case where more than two images are provided, we further propose a simple yet effective global alignment strategy that expresses all pairwise pointmaps in a common reference frame. We base our network architecture on standard Transformer encoders and decoders, allowing us to leverage powerful pretrained models. Our formulation directly provides a 3D model of the scene as well as depth information, but interestingly, we can seamlessly recover from it, pixel matches, relative and absolute camera. Exhaustive experiments on all these tasks showcase that the proposed DUSt3R can unify various 3D vision tasks and set new SoTAs on monocular/multi-view depth estimation as well as relative pose estimation. In summary, DUSt3R makes many geometric 3D vision tasks easy.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

In this article, we develop an asymptotic method for constructing confidence regions for the set of all linear subspaces arising from PCA, from which we derive hypothesis tests on this set. Our method is based on the geometry of Riemannian manifolds with which some sets of linear subspaces are endowed.

The quantum geometric tensor (QGT) is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena. The traditional QGT, defined only for pure states, has limited applicability in realistic scenarios where mixed states are common. To address this limitation, we generalize the definition of the QGT to mixed states using the purification bundle and the covariant derivative. Notably, our proposed definition reduces to the traditional QGT when mixed states approach pure states. In our framework, the real and imaginary parts of this generalized QGT correspond to the Bures metric and the mean gauge curvature, respectively, endowing it with a broad range of potential applications. Additionally, using our proposed mixed-state QGT (MSQGT), we derive the geodesic equation applicable to mixed states. This work establishes a unified framework for the geometric analysis of both pure and mixed states, thereby deepening our understanding of the geometric properties of quantum states.

With Neural Radiance Fields (NeRFs) arising as a powerful 3D representation, research has investigated its various downstream tasks, including inpainting NeRFs with 2D images. Despite successful efforts addressing the view consistency and geometry quality, prior methods yet suffer from occlusion in NeRF inpainting tasks, where 2D prior is severely limited in forming a faithful reconstruction of the scene to inpaint. To address this, we propose a novel approach that enables cross-view information sharing during knowledge distillation from a diffusion model, effectively propagating occluded information across limited views. Additionally, to align the distillation direction across multiple sampled views, we apply a grid-based denoising strategy and incorporate additional rendered views to enhance cross-view consistency. To assess our approach's capability of handling occlusion cases, we construct a dataset consisting of challenging scenes with severe occlusion, in addition to existing datasets. Compared with baseline methods, our method demonstrates better performance in cross-view consistency and faithfulness in reconstruction, while preserving high rendering quality and fidelity.

Point cloud registration approaches often fail when the overlap between point clouds is low due to noisy point correspondences. This work introduces a novel cross-attention mechanism tailored for Transformer-based architectures that tackles this problem, by fusing information from coordinates and features at the super-point level between point clouds. This formulation has remained unexplored primarily because it must guarantee rotation and translation invariance since point clouds reside in different and independent reference frames. We integrate the Gromov-Wasserstein distance into the cross-attention formulation to jointly compute distances between points across different point clouds and account for their geometric structure. By doing so, points from two distinct point clouds can attend to each other under arbitrary rigid transformations. At the point level, we also devise a self-attention mechanism that aggregates the local geometric structure information into point features for fine matching. Our formulation boosts the number of inlier correspondences, thereby yielding more precise registration results compared to state-of-the-art approaches. We have conducted an extensive evaluation on 3DMatch, 3DLoMatch, KITTI, and 3DCSR datasets.

We present GeoManip, a framework to enable generalist robots to leverage essential conditions derived from object and part relationships, as geometric constraints, for robot manipulation. For example, cutting the carrot requires adhering to a geometric constraint: the blade of the knife should be perpendicular to the carrot's direction. By interpreting these constraints through symbolic language representations and translating them into low-level actions, GeoManip bridges the gap between natural language and robotic execution, enabling greater generalizability across diverse even unseen tasks, objects, and scenarios. Unlike vision-language-action models that require extensive training, operates training-free by utilizing large foundational models: a constraint generation module that predicts stage-specific geometric constraints and a geometry parser that identifies object parts involved in these constraints. A solver then optimizes trajectories to satisfy inferred constraints from task descriptions and the scene. Furthermore, GeoManip learns in-context and provides five appealing human-robot interaction features: on-the-fly policy adaptation, learning from human demonstrations, learning from failure cases, long-horizon action planning, and efficient data collection for imitation learning. Extensive evaluations on both simulations and real-world scenarios demonstrate GeoManip's state-of-the-art performance, with superior out-of-distribution generalization while avoiding costly model training.

Diffusion models are among the most effective methods for image generation. This is in particular because, unlike GANs, they can be easily conditioned during training to produce elements with desired class or properties. However, guiding a pre-trained diffusion model to generate elements from previously unlabeled data is significantly more challenging. One of the possible solutions was given by the ADM-G guiding approach. Although ADM-G successfully generates elements from the given class, there is a significant quality gap compared to a model originally conditioned on this class. In particular, the FID score obtained by the ADM-G-guided diffusion model is nearly three times lower than the class-conditioned guidance. We demonstrate that this issue is partly due to ADM-G providing minimal guidance during the final stage of the denoising process. To address this problem, we propose GeoGuide, a guidance model based on tracing the distance of the diffusion model's trajectory from the data manifold. The main idea of GeoGuide is to produce normalized adjustments during the backward denoising process. As shown in the experiments, GeoGuide surpasses the probabilistic approach ADM-G with respect to both the FID scores and the quality of the generated images.

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.

The inference of topological principles is a key problem in structured reconstruction. We observe that wrongly predicted topological relationships are often incurred by the lack of holistic geometry clues in low-level features. Inspired by the fact that massive signals can be compactly described with frequency analysis, we experimentally explore the efficiency and tendency of learning structure geometry in the frequency domain. Accordingly, we propose a frequency-domain feature learning strategy (F-Learn) to fuse scattered geometric fragments holistically for topology-intact structure reasoning. Benefiting from the parsimonious design, the F-Learn strategy can be easily deployed into a deep reconstructor with a lightweight model modification. Experiments demonstrate that the F-Learn strategy can effectively introduce structure awareness into geometric primitive detection and topology inference, bringing significant performance improvement to final structured reconstruction. Code and pre-trained models are available at https://github.com/Geo-Tell/F-Learn.

While impressive progress has recently been made in image-oriented facial attribute translation, shape-oriented 3D facial attribute translation remains an unsolved issue. This is primarily limited by the lack of 3D generative models and ineffective usage of 3D facial data. We propose a learning framework for 3D facial attribute translation to relieve these limitations. Firstly, we customize a novel geometric map for 3D shape representation and embed it in an end-to-end generative adversarial network. The geometric map represents 3D shapes symmetrically on a square image grid, while preserving the neighboring relationship of 3D vertices in a local least-square sense. This enables effective learning for the latent representation of data with different attributes. Secondly, we employ a unified and unpaired learning framework for multi-domain attribute translation. It not only makes effective usage of data correlation from multiple domains, but also mitigates the constraint for hardly accessible paired data. Finally, we propose a hierarchical architecture for the discriminator to guarantee robust results against both global and local artifacts. We conduct extensive experiments to demonstrate the advantage of the proposed framework over the state-of-the-art in generating high-fidelity facial shapes. Given an input 3D facial shape, the proposed framework is able to synthesize novel shapes of different attributes, which covers some downstream applications, such as expression transfer, gender translation, and aging. Code at https://github.com/NaughtyZZ/3D_facial_shape_attribute_translation_ssgmap.

Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing and has recently gained popularity in machine learning, particularly in methods that preserve the graph spectrum. This work studies graph coarsening from a different perspective, developing a theory for preserving graph distances and proposing a method to achieve this. The geometric approach is useful when working with a collection of graphs, such as in graph classification and regression. In this study, we consider a graph as an element on a metric space equipped with the Gromov--Wasserstein (GW) distance, and bound the difference between the distance of two graphs and their coarsened versions. Minimizing this difference can be done using the popular weighted kernel K-means method, which improves existing spectrum-preserving methods with the proper choice of the kernel. The study includes a set of experiments to support the theory and method, including approximating the GW distance, preserving the graph spectrum, classifying graphs using spectral information, and performing regression using graph convolutional networks. Code is available at https://github.com/ychen-stat-ml/GW-Graph-Coarsening .

Computational RNA design tasks are often posed as inverse problems, where sequences are designed based on adopting a single desired secondary structure without considering 3D geometry and conformational diversity. We introduce gRNAde, a geometric RNA design pipeline operating on 3D RNA backbones to design sequences that explicitly account for structure and dynamics. Under the hood, gRNAde is a multi-state Graph Neural Network that generates candidate RNA sequences conditioned on one or more 3D backbone structures where the identities of the bases are unknown. On a single-state fixed backbone re-design benchmark of 14 RNA structures from the PDB identified by Das et al. [2010], gRNAde obtains higher native sequence recovery rates (56% on average) compared to Rosetta (45% on average), taking under a second to produce designs compared to the reported hours for Rosetta. We further demonstrate the utility of gRNAde on a new benchmark of multi-state design for structurally flexible RNAs, as well as zero-shot ranking of mutational fitness landscapes in a retrospective analysis of a recent ribozyme. Open source code: https://github.com/chaitjo/geometric-rna-design

This paper introduces a new interpretation of the Variational Autoencoder framework by taking a fully geometric point of view. We argue that vanilla VAE models unveil naturally a Riemannian structure in their latent space and that taking into consideration those geometrical aspects can lead to better interpolations and an improved generation procedure. This new proposed sampling method consists in sampling from the uniform distribution deriving intrinsically from the learned Riemannian latent space and we show that using this scheme can make a vanilla VAE competitive and even better than more advanced versions on several benchmark datasets. Since generative models are known to be sensitive to the number of training samples we also stress the method's robustness in the low data regime.

Learning a dense 3D model with fine-scale details from a single facial image is highly challenging and ill-posed. To address this problem, many approaches fit smooth geometries through facial prior while learning details as additional displacement maps or personalized basis. However, these techniques typically require vast datasets of paired multi-view data or 3D scans, whereas such datasets are scarce and expensive. To alleviate heavy data dependency, we present a robust texture-guided geometric detail recovery approach using only a single in-the-wild facial image. More specifically, our method combines high-quality texture completion with the powerful expressiveness of implicit surfaces. Initially, we inpaint occluded facial parts, generate complete textures, and build an accurate multi-view dataset of the same subject. In order to estimate the detailed geometry, we define an implicit signed distance function and employ a physically-based implicit renderer to reconstruct fine geometric details from the generated multi-view images. Our method not only recovers accurate facial details but also decomposes normals, albedos, and shading parts in a self-supervised way. Finally, we register the implicit shape details to a 3D Morphable Model template, which can be used in traditional modeling and rendering pipelines. Extensive experiments demonstrate that the proposed approach can reconstruct impressive facial details from a single image, especially when compared with state-of-the-art methods trained on large datasets.

Deep learning has improved vanishing point detection in images. Yet, deep networks require expensive annotated datasets trained on costly hardware and do not generalize to even slightly different domains, and minor problem variants. Here, we address these issues by injecting deep vanishing point detection networks with prior knowledge. This prior knowledge no longer needs to be learned from data, saving valuable annotation efforts and compute, unlocking realistic few-sample scenarios, and reducing the impact of domain changes. Moreover, the interpretability of the priors allows to adapt deep networks to minor problem variations such as switching between Manhattan and non-Manhattan worlds. We seamlessly incorporate two geometric priors: (i) Hough Transform -- mapping image pixels to straight lines, and (ii) Gaussian sphere -- mapping lines to great circles whose intersections denote vanishing points. Experimentally, we ablate our choices and show comparable accuracy to existing models in the large-data setting. We validate our model's improved data efficiency, robustness to domain changes, adaptability to non-Manhattan settings.

Predicting how a drug-like molecule binds to a specific protein target is a core problem in drug discovery. An extremely fast computational binding method would enable key applications such as fast virtual screening or drug engineering. Existing methods are computationally expensive as they rely on heavy candidate sampling coupled with scoring, ranking, and fine-tuning steps. We challenge this paradigm with EquiBind, an SE(3)-equivariant geometric deep learning model performing direct-shot prediction of both i) the receptor binding location (blind docking) and ii) the ligand's bound pose and orientation. EquiBind achieves significant speed-ups and better quality compared to traditional and recent baselines. Further, we show extra improvements when coupling it with existing fine-tuning techniques at the cost of increased running time. Finally, we propose a novel and fast fine-tuning model that adjusts torsion angles of a ligand's rotatable bonds based on closed-form global minima of the von Mises angular distance to a given input atomic point cloud, avoiding previous expensive differential evolution strategies for energy minimization.

We investigate the problem of training generative models on a very sparse collection of 3D models. We use geometrically motivated energies to augment and thus boost a sparse collection of example (training) models. We analyze the Hessian of the as-rigid-as-possible (ARAP) energy to sample from and project to the underlying (local) shape space, and use the augmented dataset to train a variational autoencoder (VAE). We iterate the process of building latent spaces of VAE and augmenting the associated dataset, to progressively reveal a richer and more expressive generative space for creating geometrically and semantically valid samples. Our framework allows us to train generative 3D models even with a small set of good quality 3D models, which are typically hard to curate. We extensively evaluate our method against a set of strong baselines, provide ablation studies and demonstrate application towards establishing shape correspondences. We present multiple examples of interesting and meaningful shape variations even when starting from as few as 3-10 training shapes.

The exploitation of syntactic graphs (SyGs) as a word's context has been shown to be beneficial for distributional semantic models (DSMs), both at the level of individual word representations and in deriving phrasal representations via composition. However, notwithstanding the potential performance benefit, the syntactically-aware DSMs proposed to date have huge numbers of parameters (compared to conventional DSMs) and suffer from data sparsity. Furthermore, the encoding of the SyG links (i.e., the syntactic relations) has been largely limited to linear maps. The knowledge graphs' literature, on the other hand, has proposed light-weight models employing different geometric transformations (GTs) to encode edges in a knowledge graph (KG). Our work explores the possibility of adopting this family of models to encode SyGs. Furthermore, we investigate which GT better encodes syntactic relations, so that these representations can be used to enhance phrase-level composition via syntactic contextualisation.

Previous research has investigated the application of Multimodal Large Language Models (MLLMs) in understanding 3D scenes by interpreting them as videos. These approaches generally depend on comprehensive 3D data inputs, such as point clouds or reconstructed Bird's-Eye View (BEV) maps. In our research, we advance this field by enhancing the capability of MLLMs to understand and reason in 3D spaces directly from video data, without the need for additional 3D input. We propose a novel and efficient method, the Video-3D Geometry Large Language Model (VG LLM). Our approach employs a 3D visual geometry encoder that extracts 3D prior information from video sequences. This information is integrated with visual tokens and fed into the MLLM. Extensive experiments have shown that our method has achieved substantial improvements in various tasks related to 3D scene understanding and spatial reasoning, all directly learned from video sources. Impressively, our 4B model, which does not rely on explicit 3D data inputs, achieves competitive results compared to existing state-of-the-art methods, and even surpasses the Gemini-1.5-Pro in the VSI-Bench evaluations.

We present WonderWorld, a novel framework for interactive 3D scene generation that enables users to interactively specify scene contents and layout and see the created scenes in low latency. The major challenge lies in achieving fast generation of 3D scenes. Existing scene generation approaches fall short of speed as they often require (1) progressively generating many views and depth maps, and (2) time-consuming optimization of the scene geometry representations. We introduce the Fast Layered Gaussian Surfels (FLAGS) as our scene representation and an algorithm to generate it from a single view. Our approach does not need multiple views, and it leverages a geometry-based initialization that significantly reduces optimization time. Another challenge is generating coherent geometry that allows all scenes to be connected. We introduce the guided depth diffusion that allows partial conditioning of depth estimation. WonderWorld generates connected and diverse 3D scenes in less than 10 seconds on a single A6000 GPU, enabling real-time user interaction and exploration. We demonstrate the potential of WonderWorld for user-driven content creation and exploration in virtual environments. We will release full code and software for reproducibility. Project website: https://kovenyu.com/WonderWorld/.

We present a novel generative 3D modeling system, coined CraftsMan, which can generate high-fidelity 3D geometries with highly varied shapes, regular mesh topologies, and detailed surfaces, and, notably, allows for refining the geometry in an interactive manner. Despite the significant advancements in 3D generation, existing methods still struggle with lengthy optimization processes, irregular mesh topologies, noisy surfaces, and difficulties in accommodating user edits, consequently impeding their widespread adoption and implementation in 3D modeling software. Our work is inspired by the craftsman, who usually roughs out the holistic figure of the work first and elaborates the surface details subsequently. Specifically, we employ a 3D native diffusion model, which operates on latent space learned from latent set-based 3D representations, to generate coarse geometries with regular mesh topology in seconds. In particular, this process takes as input a text prompt or a reference image and leverages a powerful multi-view (MV) diffusion model to generate multiple views of the coarse geometry, which are fed into our MV-conditioned 3D diffusion model for generating the 3D geometry, significantly improving robustness and generalizability. Following that, a normal-based geometry refiner is used to significantly enhance the surface details. This refinement can be performed automatically, or interactively with user-supplied edits. Extensive experiments demonstrate that our method achieves high efficacy in producing superior-quality 3D assets compared to existing methods. HomePage: https://craftsman3d.github.io/, Code: https://github.com/wyysf-98/CraftsMan

3D Gaussian Splatting (3DGS) has recently emerged as a pioneering approach in explicit scene rendering and computer graphics. Unlike traditional neural radiance field (NeRF) methods, which typically rely on implicit, coordinate-based models to map spatial coordinates to pixel values, 3DGS utilizes millions of learnable 3D Gaussians. Its differentiable rendering technique and inherent capability for explicit scene representation and manipulation positions 3DGS as a potential game-changer for the next generation of 3D reconstruction and representation technologies. This enables 3DGS to deliver real-time rendering speeds while offering unparalleled editability levels. However, despite its advantages, 3DGS suffers from substantial memory and storage requirements, posing challenges for deployment on resource-constrained devices. In this survey, we provide a comprehensive overview focusing on the scalability and compression of 3DGS. We begin with a detailed background overview of 3DGS, followed by a structured taxonomy of existing compression methods. Additionally, we analyze and compare current methods from the topological perspective, evaluating their strengths and limitations in terms of fidelity, compression ratios, and computational efficiency. Furthermore, we explore how advancements in efficient NeRF representations can inspire future developments in 3DGS optimization. Finally, we conclude with current research challenges and highlight key directions for future exploration.

Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly competitive baseline results from combining popular clustering algorithms with recent improvements in 3D geometry estimation. However, such purely geometric methods are understandably oblivious to plane semantics, which are crucial to discerning distinct planes. To overcome this limitation, we propose a method that predicts multi-view consistent plane embeddings that complement geometry when clustering points into planes. We show through extensive evaluation on the ScanNetV2 dataset that our new method outperforms existing approaches and our strong geometric baseline for the task of plane estimation.