What's the score? Automated Denoising Score Matching for Nonlinear Diffusions

TL;DR

This paper introduces local-DSM, a novel method for training score-based models on nonlinear diffusion processes, enabling applications beyond Gaussian priors in generative modeling and physics.

Contribution

It presents local-DSM, a new tractable denoising score matching objective that handles nonlinear diffusion processes using local increments and Taylor expansions.

Findings

Successfully trained generative models with non-Gaussian priors.

Demonstrated score learning for nonlinear processes in statistical physics.

Applied to CIFAR10, showing practical effectiveness.

Abstract

Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a Gaussian stationary distribution. This limits the kinds of models that can be built to those that target a Gaussian prior or more generally limits the kinds of problems that can be generically solved to those that have conditionally linear score functions. In this work, we introduce a family of tractable denoising score matching objectives, called local-DSM, built using local increments of the diffusion process. We show how local-DSM melded with Taylor expansions enables automated training and score estimation with nonlinear diffusion processes. To demonstrate these ideas, we use automated-DSM to train generative models using non-Gaussian priors on challenging low dimensional distributions and the CIFAR10 image dataset. Additionally, we use the automated-DSM to learn the scores for nonlinear processes studied in statistical physics.