Daily Papers

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being sampled onto a uniform physical grid suffer significant aliasing error and information loss. Moreover, signals can exist in different topological structures as, for example, points, lines, surfaces and volumes. It has been challenging to analyze signals with mixed topologies (for example, point cloud with surface mesh). To this end, we develop mathematical formulations for Non-Uniform Fourier Transforms (NUFT) to directly, and optimally, sample nonuniform data signals of different topologies defined on a simplex mesh into the spectral domain with no spatial sampling error. The spectral transform is performed in the Euclidean space, which removes the translation ambiguity from works on the graph spectrum. Our representation has four distinct advantages: (1) the process causes no spatial sampling error during the initial sampling, (2) the generality of this approach provides a unified framework for using CNNs to analyze signals of mixed topologies, (3) it allows us to leverage state-of-the-art backbone CNN architectures for effective learning without having to design a particular architecture for a particular data structure in an ad-hoc fashion, and (4) the representation allows weighted meshes where each element has a different weight (i.e., texture) indicating local properties. We achieve results on par with the state-of-the-art for the 3D shape retrieval task, and a new state-of-the-art for the point cloud to surface reconstruction task.

Grid-based structures are commonly used to encode explicit features for graphics primitives such as images, signed distance functions (SDF), and neural radiance fields (NeRF) due to their simple implementation. However, in n-dimensional space, calculating the value of a sampled point requires interpolating the values of its 2^n neighboring vertices. The exponential scaling with dimension leads to significant computational overheads. To address this issue, we propose a simplex-based approach for encoding graphics primitives. The number of vertices in a simplex-based structure increases linearly with dimension, making it a more efficient and generalizable alternative to grid-based representations. Using the non-axis-aligned simplicial structure property, we derive and prove a coordinate transformation, simplicial subdivision, and barycentric interpolation scheme for efficient sampling, which resembles transformation procedures in the simplex noise algorithm. Finally, we use hash tables to store multiresolution features of all interest points in the simplicial grid, which are passed into a tiny fully connected neural network to parameterize graphics primitives. We implemented a detailed simplex-based structure encoding algorithm in C++ and CUDA using the methods outlined in our approach. In the 2D image fitting task, the proposed method is capable of fitting a giga-pixel image with 9.4% less time compared to the baseline method proposed by instant-ngp, while maintaining the same quality and compression rate. In the volumetric rendering setup, we observe a maximum 41.2% speedup when the samples are dense enough.

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.

Meshes are fundamental representations of 3D surfaces. However, creating high-quality meshes is a labor-intensive task that requires significant time and expertise in 3D modeling. While a delicate object often requires over 10^4 faces to be accurately modeled, recent attempts at generating artist-like meshes are limited to 1.6K faces and heavy discretization of vertex coordinates. Hence, scaling both the maximum face count and vertex coordinate resolution is crucial to producing high-quality meshes of realistic, complex 3D objects. We present Meshtron, a novel autoregressive mesh generation model able to generate meshes with up to 64K faces at 1024-level coordinate resolution --over an order of magnitude higher face count and 8{times} higher coordinate resolution than current state-of-the-art methods. Meshtron's scalability is driven by four key components: (1) an hourglass neural architecture, (2) truncated sequence training, (3) sliding window inference, (4) a robust sampling strategy that enforces the order of mesh sequences. This results in over 50{%} less training memory, 2.5{times} faster throughput, and better consistency than existing works. Meshtron generates meshes of detailed, complex 3D objects at unprecedented levels of resolution and fidelity, closely resembling those created by professional artists, and opening the door to more realistic generation of detailed 3D assets for animation, gaming, and virtual environments.

Learning radiance fields (NeRF) with powerful 2D diffusion models has garnered popularity for text-to-3D generation. Nevertheless, the implicit 3D representations of NeRF lack explicit modeling of meshes and textures over surfaces, and such surface-undefined way may suffer from the issues, e.g., noisy surfaces with ambiguous texture details or cross-view inconsistency. To alleviate this, we present DreamMesh, a novel text-to-3D architecture that pivots on well-defined surfaces (triangle meshes) to generate high-fidelity explicit 3D model. Technically, DreamMesh capitalizes on a distinctive coarse-to-fine scheme. In the coarse stage, the mesh is first deformed by text-guided Jacobians and then DreamMesh textures the mesh with an interlaced use of 2D diffusion models in a tuning free manner from multiple viewpoints. In the fine stage, DreamMesh jointly manipulates the mesh and refines the texture map, leading to high-quality triangle meshes with high-fidelity textured materials. Extensive experiments demonstrate that DreamMesh significantly outperforms state-of-the-art text-to-3D methods in faithfully generating 3D content with richer textual details and enhanced geometry. Our project page is available at https://dreammesh.github.io.

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.

Given a K-vertex simplex in a d-dimensional space, suppose we measure n points on the simplex with noise (hence, some of the observed points fall outside the simplex). Vertex hunting is the problem of estimating the K vertices of the simplex. A popular vertex hunting algorithm is successive projection algorithm (SPA). However, SPA is observed to perform unsatisfactorily under strong noise or outliers. We propose pseudo-point SPA (pp-SPA). It uses a projection step and a denoise step to generate pseudo-points and feed them into SPA for vertex hunting. We derive error bounds for pp-SPA, leveraging on extreme value theory of (possibly) high-dimensional random vectors. The results suggest that pp-SPA has faster rates and better numerical performances than SPA. Our analysis includes an improved non-asymptotic bound for the original SPA, which is of independent interest.

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.

We introduce Amortized Text-to-Mesh (AToM), a feed-forward text-to-mesh framework optimized across multiple text prompts simultaneously. In contrast to existing text-to-3D methods that often entail time-consuming per-prompt optimization and commonly output representations other than polygonal meshes, AToM directly generates high-quality textured meshes in less than 1 second with around 10 times reduction in the training cost, and generalizes to unseen prompts. Our key idea is a novel triplane-based text-to-mesh architecture with a two-stage amortized optimization strategy that ensures stable training and enables scalability. Through extensive experiments on various prompt benchmarks, AToM significantly outperforms state-of-the-art amortized approaches with over 4 times higher accuracy (in DF415 dataset) and produces more distinguishable and higher-quality 3D outputs. AToM demonstrates strong generalizability, offering finegrained 3D assets for unseen interpolated prompts without further optimization during inference, unlike per-prompt solutions.

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.

Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.

In this work, we develop intuitive controls for editing the style of 3D objects. Our framework, Text2Mesh, stylizes a 3D mesh by predicting color and local geometric details which conform to a target text prompt. We consider a disentangled representation of a 3D object using a fixed mesh input (content) coupled with a learned neural network, which we term neural style field network. In order to modify style, we obtain a similarity score between a text prompt (describing style) and a stylized mesh by harnessing the representational power of CLIP. Text2Mesh requires neither a pre-trained generative model nor a specialized 3D mesh dataset. It can handle low-quality meshes (non-manifold, boundaries, etc.) with arbitrary genus, and does not require UV parameterization. We demonstrate the ability of our technique to synthesize a myriad of styles over a wide variety of 3D meshes.

The polygon mesh representation of 3D data exhibits great flexibility, fast rendering speed, and storage efficiency, which is widely preferred in various applications. However, given its unstructured graph representation, the direct generation of high-fidelity 3D meshes is challenging. Fortunately, with a pre-defined ordering strategy, 3D meshes can be represented as sequences, and the generation process can be seamlessly treated as an auto-regressive problem. In this paper, we validate the Neural Coordinate Field (NeurCF), an explicit coordinate representation with implicit neural embeddings, is a simple-yet-effective representation for large-scale sequential mesh modeling. After that, we present MeshXL, a family of generative pre-trained auto-regressive models, which addresses the process of 3D mesh generation with modern large language model approaches. Extensive experiments show that MeshXL is able to generate high-quality 3D meshes, and can also serve as foundation models for various down-stream applications.

Mesh generation has become a critical topic in recent years, forming the foundation of all 3D objects used across various applications, such as virtual reality, gaming, and 3D printing. With advancements in computational resources and machine learning, neural networks have emerged as powerful tools for generating high-quality 3D object representations, enabling accurate scene and object reconstructions. Despite these advancements, many methods produce meshes that lack realism or exhibit geometric and textural flaws, necessitating additional processing to improve their quality. This research introduces a convex optimization programming called disciplined convex programming to enhance existing meshes by refining their texture and geometry with a conic solver. By focusing on a sparse set of point clouds from both the original and target meshes, this method demonstrates significant improvements in mesh quality with minimal data requirements. To evaluate the approach, the classical dolphin mesh dataset from Facebook AI was used as a case study, with optimization performed using the CVXPY library. The results reveal promising potential for streamlined and effective mesh refinement.

Image-based 3D reconstruction has increasingly stunning results over the past few years with the latest improvements in computer vision and graphics. Geometry and topology are two fundamental concepts when dealing with 3D mesh structures. But the latest often remains a side issue in the 3D mesh-based reconstruction literature. Indeed, performing per-vertex elementary displacements over a 3D sphere mesh only impacts its geometry and leaves the topological structure unchanged and fixed. Whereas few attempts propose to update the geometry and the topology, all need to lean on costly 3D ground-truth to determine the faces/edges to prune. We present in this work a method that aims to refine the topology of any 3D mesh through a face-pruning strategy that extensively relies upon 2D alpha masks and camera pose information. Our solution leverages a differentiable renderer that renders each face as a 2D soft map. Its pixel intensity reflects the probability of being covered during the rendering process by such a face. Based on the 2D soft-masks available, our method is thus able to quickly highlight all the incorrectly rendered faces for a given viewpoint. Because our module is agnostic to the network that produces the 3D mesh, it can be easily plugged into any self-supervised image-based (either synthetic or natural) 3D reconstruction pipeline to get complex meshes with a non-spherical topology.

We present InstantMesh, a feed-forward framework for instant 3D mesh generation from a single image, featuring state-of-the-art generation quality and significant training scalability. By synergizing the strengths of an off-the-shelf multiview diffusion model and a sparse-view reconstruction model based on the LRM architecture, InstantMesh is able to create diverse 3D assets within 10 seconds. To enhance the training efficiency and exploit more geometric supervisions, e.g, depths and normals, we integrate a differentiable iso-surface extraction module into our framework and directly optimize on the mesh representation. Experimental results on public datasets demonstrate that InstantMesh significantly outperforms other latest image-to-3D baselines, both qualitatively and quantitatively. We release all the code, weights, and demo of InstantMesh, with the intention that it can make substantial contributions to the community of 3D generative AI and empower both researchers and content creators.

Triangle meshes play a crucial role in 3D applications for efficient manipulation and rendering. While auto-regressive methods generate structured meshes by predicting discrete vertex tokens, they are often constrained by limited face counts and mesh incompleteness. To address these challenges, we propose DeepMesh, a framework that optimizes mesh generation through two key innovations: (1) an efficient pre-training strategy incorporating a novel tokenization algorithm, along with improvements in data curation and processing, and (2) the introduction of Reinforcement Learning (RL) into 3D mesh generation to achieve human preference alignment via Direct Preference Optimization (DPO). We design a scoring standard that combines human evaluation with 3D metrics to collect preference pairs for DPO, ensuring both visual appeal and geometric accuracy. Conditioned on point clouds and images, DeepMesh generates meshes with intricate details and precise topology, outperforming state-of-the-art methods in both precision and quality. Project page: https://zhaorw02.github.io/DeepMesh/

Flow matching in the continuous simplex has emerged as a promising strategy for DNA sequence design, but struggles to scale to higher simplex dimensions required for peptide and protein generation. We introduce Gumbel-Softmax Flow and Score Matching, a generative framework on the simplex based on a novel Gumbel-Softmax interpolant with a time-dependent temperature. Using this interpolant, we introduce Gumbel-Softmax Flow Matching by deriving a parameterized velocity field that transports from smooth categorical distributions to distributions concentrated at a single vertex of the simplex. We alternatively present Gumbel-Softmax Score Matching which learns to regress the gradient of the probability density. Our framework enables high-quality, diverse generation and scales efficiently to higher-dimensional simplices. To enable training-free guidance, we propose Straight-Through Guided Flows (STGFlow), a classifier-based guidance method that leverages straight-through estimators to steer the unconditional velocity field toward optimal vertices of the simplex. STGFlow enables efficient inference-time guidance using classifiers pre-trained on clean sequences, and can be used with any discrete flow method. Together, these components form a robust framework for controllable de novo sequence generation. We demonstrate state-of-the-art performance in conditional DNA promoter design, sequence-only protein generation, and target-binding peptide design for rare disease treatment.

We introduce MeshAnything V2, an autoregressive transformer that generates Artist-Created Meshes (AM) aligned to given shapes. It can be integrated with various 3D asset production pipelines to achieve high-quality, highly controllable AM generation. MeshAnything V2 surpasses previous methods in both efficiency and performance using models of the same size. These improvements are due to our newly proposed mesh tokenization method: Adjacent Mesh Tokenization (AMT). Different from previous methods that represent each face with three vertices, AMT uses a single vertex whenever possible. Compared to previous methods, AMT requires about half the token sequence length to represent the same mesh in average. Furthermore, the token sequences from AMT are more compact and well-structured, fundamentally benefiting AM generation. Our extensive experiments show that AMT significantly improves the efficiency and performance of AM generation. Project Page: https://buaacyw.github.io/meshanything-v2/

Text-driven 3D stylization is a complex and crucial task in the fields of computer vision (CV) and computer graphics (CG), aimed at transforming a bare mesh to fit a target text. Prior methods adopt text-independent multilayer perceptrons (MLPs) to predict the attributes of the target mesh with the supervision of CLIP loss. However, such text-independent architecture lacks textual guidance during predicting attributes, thus leading to unsatisfactory stylization and slow convergence. To address these limitations, we present X-Mesh, an innovative text-driven 3D stylization framework that incorporates a novel Text-guided Dynamic Attention Module (TDAM). The TDAM dynamically integrates the guidance of the target text by utilizing text-relevant spatial and channel-wise attentions during vertex feature extraction, resulting in more accurate attribute prediction and faster convergence speed. Furthermore, existing works lack standard benchmarks and automated metrics for evaluation, often relying on subjective and non-reproducible user studies to assess the quality of stylized 3D assets. To overcome this limitation, we introduce a new standard text-mesh benchmark, namely MIT-30, and two automated metrics, which will enable future research to achieve fair and objective comparisons. Our extensive qualitative and quantitative experiments demonstrate that X-Mesh outperforms previous state-of-the-art methods.

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous representation for meshes with fixed topology, a common and practical setting in many faces-, hand-, and body-related applications. First, we split the template into multiple closed manifold genus-0 meshes so that each genus-0 mesh can be parameterized onto the unit sphere. Then we learn spherical implicit surface (SIS), which takes a spherical coordinate and a global feature or a set of local features around the coordinate as inputs, predicting the vertex corresponding to the coordinate as an output. Since the spherical coordinates are continuous, SIS can depict a mesh in an arbitrary resolution. SIS representation builds a bridge between discrete and continuous representation in 3D shapes. Specifically, we train SIS networks in a self-supervised manner for two tasks: a reconstruction task and a super-resolution task. Experiments show that our SIS representation is comparable with state-of-the-art methods that are specifically designed for meshes with a fixed resolution and significantly outperforms methods that work in arbitrary resolutions.

We propose MeshLRM, a novel LRM-based approach that can reconstruct a high-quality mesh from merely four input images in less than one second. Different from previous large reconstruction models (LRMs) that focus on NeRF-based reconstruction, MeshLRM incorporates differentiable mesh extraction and rendering within the LRM framework. This allows for end-to-end mesh reconstruction by fine-tuning a pre-trained NeRF LRM with mesh rendering. Moreover, we improve the LRM architecture by simplifying several complex designs in previous LRMs. MeshLRM's NeRF initialization is sequentially trained with low- and high-resolution images; this new LRM training strategy enables significantly faster convergence and thereby leads to better quality with less compute. Our approach achieves state-of-the-art mesh reconstruction from sparse-view inputs and also allows for many downstream applications, including text-to-3D and single-image-to-3D generation. Project page: https://sarahweiii.github.io/meshlrm/

This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry, generative modeling, and inverse physics. Existing implementations adapt classic isosurface extraction algorithms like Marching Cubes or Dual Contouring; these techniques were designed to extract meshes from fixed, known fields, and in the optimization setting they lack the degrees of freedom to represent high-quality feature-preserving meshes, or suffer from numerical instabilities. We introduce FlexiCubes, an isosurface representation specifically designed for optimizing an unknown mesh with respect to geometric, visual, or even physical objectives. Our main insight is to introduce additional carefully-chosen parameters into the representation, which allow local flexible adjustments to the extracted mesh geometry and connectivity. These parameters are updated along with the underlying scalar field via automatic differentiation when optimizing for a downstream task. We base our extraction scheme on Dual Marching Cubes for improved topological properties, and present extensions to optionally generate tetrahedral and hierarchically-adaptive meshes. Extensive experiments validate FlexiCubes on both synthetic benchmarks and real-world applications, showing that it offers significant improvements in mesh quality and geometric fidelity.

Recent advancements in 2D/3D generative techniques have facilitated the generation of dynamic 3D objects from monocular videos. Previous methods mainly rely on the implicit neural radiance fields (NeRF) or explicit Gaussian Splatting as the underlying representation, and struggle to achieve satisfactory spatial-temporal consistency and surface appearance. Drawing inspiration from modern 3D animation pipelines, we introduce DreamMesh4D, a novel framework combining mesh representation with geometric skinning technique to generate high-quality 4D object from a monocular video. Instead of utilizing classical texture map for appearance, we bind Gaussian splats to triangle face of mesh for differentiable optimization of both the texture and mesh vertices. In particular, DreamMesh4D begins with a coarse mesh obtained through an image-to-3D generation procedure. Sparse points are then uniformly sampled across the mesh surface, and are used to build a deformation graph to drive the motion of the 3D object for the sake of computational efficiency and providing additional constraint. For each step, transformations of sparse control points are predicted using a deformation network, and the mesh vertices as well as the surface Gaussians are deformed via a novel geometric skinning algorithm, which is a hybrid approach combining LBS (linear blending skinning) and DQS (dual-quaternion skinning), mitigating drawbacks associated with both approaches. The static surface Gaussians and mesh vertices as well as the deformation network are learned via reference view photometric loss, score distillation loss as well as other regularizers in a two-stage manner. Extensive experiments demonstrate superior performance of our method. Furthermore, our method is compatible with modern graphic pipelines, showcasing its potential in the 3D gaming and film industry.

Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some methods utilize reinforcement learning or supervised learning techniques to create adaptive and dynamic meshes, due to the dynamic nature of these systems. However, these approaches face two primary challenges: (1) the need for expensive optimal mesh data, and (2) the change of the solution space's degree of freedom and topology during mesh refinement. To address these challenges, this paper proposes a neural PDE solver with a neural mesh adapter. To begin with, we introduce a novel data-free neural mesh adaptor, called Data-free Mesh Mover (DMM), with two main innovations. Firstly, it is an operator that maps the solution to adaptive meshes and is trained using the Monge-Amp\`ere equation without optimal mesh data. Secondly, it dynamically changes the mesh by moving existing nodes rather than adding or deleting nodes and edges. Theoretical analysis shows that meshes generated by DMM have the lowest interpolation error bound. Based on DMM, to efficiently and accurately model dynamic systems, we develop a moving mesh based neural PDE solver (MM-PDE) that embeds the moving mesh with a two-branch architecture and a learnable interpolation framework to preserve information within the data. Empirical experiments demonstrate that our method generates suitable meshes and considerably enhances accuracy when modeling widely considered PDE systems. The code can be found at: https://github.com/Peiyannn/MM-PDE.git.

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.

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

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s geq 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

We study the problem of few-shot physically-aware articulated mesh generation. By observing an articulated object dataset containing only a few examples, we wish to learn a model that can generate diverse meshes with high visual fidelity and physical validity. Previous mesh generative models either have difficulties in depicting a diverse data space from only a few examples or fail to ensure physical validity of their samples. Regarding the above challenges, we propose two key innovations, including 1) a hierarchical mesh deformation-based generative model based upon the divide-and-conquer philosophy to alleviate the few-shot challenge by borrowing transferrable deformation patterns from large scale rigid meshes and 2) a physics-aware deformation correction scheme to encourage physically plausible generations. We conduct extensive experiments on 6 articulated categories to demonstrate the superiority of our method in generating articulated meshes with better diversity, higher visual fidelity, and better physical validity over previous methods in the few-shot setting. Further, we validate solid contributions of our two innovations in the ablation study. Project page with code is available at https://meowuu7.github.io/few-arti-obj-gen.

We introduce MeshGPT, a new approach for generating triangle meshes that reflects the compactness typical of artist-created meshes, in contrast to dense triangle meshes extracted by iso-surfacing methods from neural fields. Inspired by recent advances in powerful large language models, we adopt a sequence-based approach to autoregressively generate triangle meshes as sequences of triangles. We first learn a vocabulary of latent quantized embeddings, using graph convolutions, which inform these embeddings of the local mesh geometry and topology. These embeddings are sequenced and decoded into triangles by a decoder, ensuring that they can effectively reconstruct the mesh. A transformer is then trained on this learned vocabulary to predict the index of the next embedding given previous embeddings. Once trained, our model can be autoregressively sampled to generate new triangle meshes, directly generating compact meshes with sharp edges, more closely imitating the efficient triangulation patterns of human-crafted meshes. MeshGPT demonstrates a notable improvement over state of the art mesh generation methods, with a 9% increase in shape coverage and a 30-point enhancement in FID scores across various categories.

This work explores expanding the capabilities of large language models (LLMs) pretrained on text to generate 3D meshes within a unified model. This offers key advantages of (1) leveraging spatial knowledge already embedded in LLMs, derived from textual sources like 3D tutorials, and (2) enabling conversational 3D generation and mesh understanding. A primary challenge is effectively tokenizing 3D mesh data into discrete tokens that LLMs can process seamlessly. To address this, we introduce LLaMA-Mesh, a novel approach that represents the vertex coordinates and face definitions of 3D meshes as plain text, allowing direct integration with LLMs without expanding the vocabulary. We construct a supervised fine-tuning (SFT) dataset enabling pretrained LLMs to (1) generate 3D meshes from text prompts, (2) produce interleaved text and 3D mesh outputs as required, and (3) understand and interpret 3D meshes. Our work is the first to demonstrate that LLMs can be fine-tuned to acquire complex spatial knowledge for 3D mesh generation in a text-based format, effectively unifying the 3D and text modalities. LLaMA-Mesh achieves mesh generation quality on par with models trained from scratch while maintaining strong text generation performance.

We introduce TetSphere Splatting, a Lagrangian geometry representation designed for high-quality 3D shape modeling. TetSphere splatting leverages an underused yet powerful geometric primitive -- volumetric tetrahedral meshes. It represents 3D shapes by deforming a collection of tetrahedral spheres, with geometric regularizations and constraints that effectively resolve common mesh issues such as irregular triangles, non-manifoldness, and floating artifacts. Experimental results on multi-view and single-view reconstruction highlight TetSphere splatting's superior mesh quality while maintaining competitive reconstruction accuracy compared to state-of-the-art methods. Additionally, TetSphere splatting demonstrates versatility by seamlessly integrating into generative modeling tasks, such as image-to-3D and text-to-3D generation.

Articulated 3D object generation is fundamental for creating realistic, functional, and interactable virtual assets which are not simply static. We introduce MeshArt, a hierarchical transformer-based approach to generate articulated 3D meshes with clean, compact geometry, reminiscent of human-crafted 3D models. We approach articulated mesh generation in a part-by-part fashion across two stages. First, we generate a high-level articulation-aware object structure; then, based on this structural information, we synthesize each part's mesh faces. Key to our approach is modeling both articulation structures and part meshes as sequences of quantized triangle embeddings, leading to a unified hierarchical framework with transformers for autoregressive generation. Object part structures are first generated as their bounding primitives and articulation modes; a second transformer, guided by these articulation structures, then generates each part's mesh triangles. To ensure coherency among generated parts, we introduce structure-guided conditioning that also incorporates local part mesh connectivity. MeshArt shows significant improvements over state of the art, with 57.1% improvement in structure coverage and a 209-point improvement in mesh generation FID.

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN, a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness of our task-driven pooling on various learning tasks applied to 3D meshes.

We introduce ReMatching, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate re-meshing paradigm, can target shape-matching tasks even on meshes counting millions of vertices, where the original functional maps does not apply or requires a massive computational cost. The core of our procedure is a time-efficient remeshing algorithm which constructs a low-resolution geometry while acting conservatively on the original topology and metric. These properties allow translating the functional maps optimization problem on the resulting low-resolution representation, thus enabling efficient computation of correspondences with functional map approaches. Finally, we propose an efficient technique for extending the estimated correspondence to the original meshes. We show that our method is more efficient and effective through quantitative and qualitative comparisons, outperforming state-of-the-art pipelines in quality and computational cost.

We present Simplex Random Features (SimRFs), a new random feature (RF) mechanism for unbiased approximation of the softmax and Gaussian kernels by geometrical correlation of random projection vectors. We prove that SimRFs provide the smallest possible mean square error (MSE) on unbiased estimates of these kernels among the class of weight-independent geometrically-coupled positive random feature (PRF) mechanisms, substantially outperforming the previously most accurate Orthogonal Random Features at no observable extra cost. We present a more computationally expensive SimRFs+ variant, which we prove is asymptotically optimal in the broader family of weight-dependent geometrical coupling schemes (which permit correlations between random vector directions and norms). In extensive empirical studies, we show consistent gains provided by SimRFs in settings including pointwise kernel estimation, nonparametric classification and scalable Transformers.

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/}.

We introduce PhysGaussian, a new method that seamlessly integrates physically grounded Newtonian dynamics within 3D Gaussians to achieve high-quality novel motion synthesis. Employing a custom Material Point Method (MPM), our approach enriches 3D Gaussian kernels with physically meaningful kinematic deformation and mechanical stress attributes, all evolved in line with continuum mechanics principles. A defining characteristic of our method is the seamless integration between physical simulation and visual rendering: both components utilize the same 3D Gaussian kernels as their discrete representations. This negates the necessity for triangle/tetrahedron meshing, marching cubes, "cage meshes," or any other geometry embedding, highlighting the principle of "what you see is what you simulate (WS^2)." Our method demonstrates exceptional versatility across a wide variety of materials--including elastic entities, metals, non-Newtonian fluids, and granular materials--showcasing its strong capabilities in creating diverse visual content with novel viewpoints and movements. Our project page is at: https://xpandora.github.io/PhysGaussian/

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

In the domain of 3D content creation, achieving optimal mesh topology through AI models has long been a pursuit for 3D artists. Previous methods, such as MeshGPT, have explored the generation of ready-to-use 3D objects via mesh auto-regressive techniques. While these methods produce visually impressive results, their reliance on token-by-token predictions in the auto-regressive process leads to several significant limitations. These include extremely slow generation speeds and an uncontrollable number of mesh faces. In this paper, we introduce MeshCraft, a novel framework for efficient and controllable mesh generation, which leverages continuous spatial diffusion to generate discrete triangle faces. Specifically, MeshCraft consists of two core components: 1) a transformer-based VAE that encodes raw meshes into continuous face-level tokens and decodes them back to the original meshes, and 2) a flow-based diffusion transformer conditioned on the number of faces, enabling the generation of high-quality 3D meshes with a predefined number of faces. By utilizing the diffusion model for the simultaneous generation of the entire mesh topology, MeshCraft achieves high-fidelity mesh generation at significantly faster speeds compared to auto-regressive methods. Specifically, MeshCraft can generate an 800-face mesh in just 3.2 seconds (35times faster than existing baselines). Extensive experiments demonstrate that MeshCraft outperforms state-of-the-art techniques in both qualitative and quantitative evaluations on ShapeNet dataset and demonstrates superior performance on Objaverse dataset. Moreover, it integrates seamlessly with existing conditional guidance strategies, showcasing its potential to relieve artists from the time-consuming manual work involved in mesh creation.

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.

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

Micro Aerial Vehicles (MAVs) that operate in unstructured, unexplored environments require fast and flexible local planning, which can replan when new parts of the map are explored. Trajectory optimization methods fulfill these needs, but require obstacle distance information, which can be given by Euclidean Signed Distance Fields (ESDFs). We propose a method to incrementally build ESDFs from Truncated Signed Distance Fields (TSDFs), a common implicit surface representation used in computer graphics and vision. TSDFs are fast to build and smooth out sensor noise over many observations, and are designed to produce surface meshes. Meshes allow human operators to get a better assessment of the robot's environment, and set high-level mission goals. We show that we can build TSDFs faster than Octomaps, and that it is more accurate to build ESDFs out of TSDFs than occupancy maps. Our complete system, called voxblox, will be available as open source and runs in real-time on a single CPU core. We validate our approach on-board an MAV, by using our system with a trajectory optimization local planner, entirely on-board and in real-time.

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased, perceptually distorted surfaces and lack scalability to high-resolution 3D shapes. We present a data-driven approach for automatic feature detection and remeshing that requires only a coarse, aliased mesh as input and scales to arbitrary resolution reconstructions. We define and learn a collection of surface-based fields to (1) capture sharp geometric features in the shape with an implicit vertexwise model and (2) approximate improvements in normals alignment obtained by applying edge-flips with an edgewise model. To support scaling to arbitrary complexity shapes, we learn our fields using local triangulated patches, fusing estimates on complete surface meshes. Our feature remeshing algorithm integrates the learned fields as sharp feature priors and optimizes vertex placement and mesh connectivity for maximum expected surface improvement. On a challenging collection of high-resolution shape reconstructions in the ABC dataset, our algorithm improves over state-of-the-art by 26% normals F-score and 42% perceptual RMSE_{v}.

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.

Recently, 3D assets created via reconstruction and generation have matched the quality of manually crafted assets, highlighting their potential for replacement. However, this potential is largely unrealized because these assets always need to be converted to meshes for 3D industry applications, and the meshes produced by current mesh extraction methods are significantly inferior to Artist-Created Meshes (AMs), i.e., meshes created by human artists. Specifically, current mesh extraction methods rely on dense faces and ignore geometric features, leading to inefficiencies, complicated post-processing, and lower representation quality. To address these issues, we introduce MeshAnything, a model that treats mesh extraction as a generation problem, producing AMs aligned with specified shapes. By converting 3D assets in any 3D representation into AMs, MeshAnything can be integrated with various 3D asset production methods, thereby enhancing their application across the 3D industry. The architecture of MeshAnything comprises a VQ-VAE and a shape-conditioned decoder-only transformer. We first learn a mesh vocabulary using the VQ-VAE, then train the shape-conditioned decoder-only transformer on this vocabulary for shape-conditioned autoregressive mesh generation. Our extensive experiments show that our method generates AMs with hundreds of times fewer faces, significantly improving storage, rendering, and simulation efficiencies, while achieving precision comparable to previous methods.

This paper aims to generate materials for 3D meshes from text descriptions. Unlike existing methods that synthesize texture maps, we propose to generate segment-wise procedural material graphs as the appearance representation, which supports high-quality rendering and provides substantial flexibility in editing. Instead of relying on extensive paired data, i.e., 3D meshes with material graphs and corresponding text descriptions, to train a material graph generative model, we propose to leverage the pre-trained 2D diffusion model as a bridge to connect the text and material graphs. Specifically, our approach decomposes a shape into a set of segments and designs a segment-controlled diffusion model to synthesize 2D images that are aligned with mesh parts. Based on generated images, we initialize parameters of material graphs and fine-tune them through the differentiable rendering module to produce materials in accordance with the textual description. Extensive experiments demonstrate the superior performance of our framework in photorealism, resolution, and editability over existing methods. Project page: https://zhanghe3z.github.io/MaPa/

We introduce MeshPad, a generative approach that creates 3D meshes from sketch inputs. Building on recent advances in artistic-designed triangle mesh generation, our approach addresses the need for interactive artistic mesh creation. To this end, we focus on enabling consistent edits by decomposing editing into 'deletion' of regions of a mesh, followed by 'addition' of new mesh geometry. Both operations are invoked by simple user edits of a sketch image, facilitating an iterative content creation process and enabling the construction of complex 3D meshes. Our approach is based on a triangle sequence-based mesh representation, exploiting a large Transformer model for mesh triangle addition and deletion. In order to perform edits interactively, we introduce a vertex-aligned speculative prediction strategy on top of our additive mesh generator. This speculator predicts multiple output tokens corresponding to a vertex, thus significantly reducing the computational cost of inference and accelerating the editing process, making it possible to execute each editing step in only a few seconds. Comprehensive experiments demonstrate that MeshPad outperforms state-of-the-art sketch-conditioned mesh generation methods, achieving more than 22% mesh quality improvement in Chamfer distance, and being preferred by 90% of participants in perceptual evaluations.