While diffusion models have achieved promising performances in data synthesis, they might suffer error propagation because of their cascade structure, where the distributional mismatch spreads and magnifies through the chain of denoising modules. However, a strict analysis is expected since many sequential models such as Conditional Random Field (CRF) are free from error propagation. In this paper, we empirically and theoretically verify that diffusion models are indeed affected by error propagation and we then propose a regularization to address this problem. Our theoretical analysis reveals that the question can be reduced to whether every denoising module of the diffusion model is fault-tolerant. We derive insightful transition equations, indicating that the module can't recover from input errors and even propagates additional errors to the next module. Our analysis directly leads to a consistency regularization scheme for diffusion models, which explicitly reduces the distribution gap between forward and backward processes. We further introduce a bootstrapping algorithm to reduce the computation cost of the regularizer. Our experimental results on multiple image datasets show that our regularization effectively handles error propagation and significantly improves the performance of vanilla diffusion models.

翻译：尽管扩散模型在数据合成方面取得了显著成效，但其级联结构可能导致分布失配沿去噪模块链传播放大，从而引发误差传播问题。然而，鉴于条件随机场等序列模型并不受误差传播影响，严谨的理论分析亟待开展。本文从经验与理论双重维度验证了扩散模型确实存在误差传播现象，并提出了相应的正则化方法。理论分析表明，该问题可归结为扩散模型中每个去噪模块的容错性。我们推导出具有洞察力的转移方程，揭示出模块无法从输入误差中恢复，甚至会向后续模块传播额外误差。该分析直接引出了面向扩散模型的一致性正则化方案，该方案能有效缩小正向与反向过程之间的分布差距。我们进一步提出自举算法以降低正则化器的计算成本。在多个图像数据集上的实验表明，所提正则化方法能有效抑制误差传播，显著提升原始扩散模型的性能。