What Secrets Do Your Manifolds Hold? Understanding the Local Geometry of Generative Models
Ahmed Imtiaz Humayun Ibtihel Amara Cristina Nader Vasconcelos Deepak Ramachandran Candice Schumann Junfeng He Katherine A Heller Golnoosh Farnadi Negar Rostamzadeh Mohammad Havaei
Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with GAN, Transformer or Diffusion architectures, generation performance can vary significantly based on which part of the learned data manifold is sampled. In this paper we study the post-training local geometry of the learned manifold and its relationship to generation outcomes for models ranging from toy settings to the latent decoder of the near state-of-the-art Stable Diffusion 1.4 Text-to-Image model. Building on the theory of continuous piecewise-linear (CPWL) generators, we characterize the local geometry in terms of three geometric descriptors - scaling ($\psi$), rank ($\nu$), and complexity ($\delta$). We provide quantitative and qualitative evidence showing that for a given latent, the local descriptors are indicative of generation aesthetics, artifacts, diversity, and memorization. Finally we demonstrate that training a reward model using the local geometry allows us to control the log-likelihood of a generated sample under the learned distribution, and improve the qualitative aspects of an image.
Geometry, Diffusion models, VAE, Generative Models, Guidance, Memorization, Out-of-Distribution Detection
We show that the local geometry of generative models is indicative of generation aesthetics, artifacts, diversity, and memorization.