Diffusion probabilistic models (DPMs) have recently shown great potential for denoising tasks. Despite their practical utility, there is a notable gap in their theoretical understanding. This paper contributes novel theoretical insights by rigorously proving the asymptotic convergence of a specific DPM denoising strategy to the mean square error (MSE)-optimal conditional mean estimator (CME) over a large number of diffusion steps. The studied DPM-based denoiser shares the training procedure of DPMs but distinguishes itself by forwarding only the conditional mean during the reverse inference process after training. We highlight the unique perspective that DPMs are composed of an asymptotically optimal denoiser while simultaneously inheriting a powerful generator by switching re-sampling in the reverse process on and off. The theoretical findings are validated by numerical results.

翻译：扩散概率模型（DPMs）近期在去噪任务中展现出巨大潜力。尽管具有实际应用价值，但其理论基础仍存在显著空白。本文通过严格证明特定DPM去噪策略在大量扩散步骤下渐近收敛于均方误差（MSE）最优的条件均值估计器（CME），提出了新颖的理论见解。所研究的基于DPM的去噪器沿用了DPM的训练流程，但在训练完成后的反向推理过程中仅前向传递条件均值。我们强调了独特视角：DPMs由渐近最优去噪器构成，同时通过切换反向过程中的重采样开关，继承了强大的生成器特性。理论发现通过数值结果得到验证。