  Although diffusion models (DMs) have shown promising performances in a number
of tasks (e.g., speech synthesis and image generation), they might suffer from
error propagation because of their sequential structure. However, this is not
certain because some sequential models, such as Conditional Random Field (CRF),
are free from this problem. To address this issue, we develop a theoretical
framework to mathematically formulate error propagation in the architecture of
DMs, The framework contains three elements, including modular error, cumulative
error, and propagation equation. The modular and cumulative errors are related
by the equation, which interprets that DMs are indeed affected by error
propagation. Our theoretical study also suggests that the cumulative error is
closely related to the generation quality of DMs. Based on this finding, we
apply the cumulative error as a regularization term to reduce error
propagation. Because the term is computationally intractable, we derive its
upper bound and design a bootstrap algorithm to efficiently estimate the bound
for optimization. We have conducted extensive experiments on multiple image
datasets, showing that our proposed regularization reduces error propagation,
significantly improves vanilla DMs, and outperforms previous baselines.
