Evaluating the design space of diffusion-based generative models

TL;DR

This paper offers a comprehensive theoretical analysis of diffusion-based generative models, covering training and sampling, and provides insights into optimal design choices for effective generation.

Contribution

It presents the first non-asymptotic convergence analysis of denoising score matching under gradient descent and refines sampling error analysis for variance exploding models.

Findings

Guides optimal noise distribution and loss weighting in training.

Provides theoretical insights on time and variance schedules in sampling.

Suggests design preferences depending on score training quality.

Abstract

Most existing theoretical investigations of the accuracy of diffusion models, albeit significant, assume the score function has been approximated to a certain accuracy, and then use this a priori bound to control the error of generation. This article instead provides a first quantitative understanding of the whole generation process, i.e., both training and sampling. More precisely, it conducts a non-asymptotic convergence analysis of denoising score matching under gradient descent. In addition, a refined sampling error analysis for variance exploding models is also provided. The combination of these two results yields a full error analysis, which elucidates (again, but this time theoretically) how to design the training and sampling processes for effective generation. For instance, our theory implies a preference toward noise distribution and loss weighting in training that qualitatively agree with the ones used in [Karras et al., 2022]. It also provides perspectives on the choices of time and variance schedules in sampling: when the score is well trained, the design in [Song et al., 2021] is more preferable, but when it is less trained, the design in [Karras et al., 2022] becomes more preferable.