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arXiv · 2406.12839

Evaluating the design space of diffusion-based generative models

Yuqing Wang·Ye He·Molei Tao
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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.

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Yuqing Wang, Ye He, Molei Tao. 2024-06-18. Evaluating the design space of diffusion-based generative models. https://arxiv.org/abs/2406.12839

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