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Bibliographic Details
Main Authors: Singhal, Raghav, Goldstein, Mark, Ranganath, Rajesh
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2407.07998
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author Singhal, Raghav
Goldstein, Mark
Ranganath, Rajesh
author_facet Singhal, Raghav
Goldstein, Mark
Ranganath, Rajesh
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_07998
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle What's the score? Automated Denoising Score Matching for Nonlinear Diffusions
Singhal, Raghav
Goldstein, Mark
Ranganath, Rajesh
Machine Learning
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.
title What's the score? Automated Denoising Score Matching for Nonlinear Diffusions
topic Machine Learning
url https://arxiv.org/abs/2407.07998