On the Asymptotic Mean Square Error Optimality of Diffusion Probabilistic Models

arXiv:2403.02957v1 Announce Type: new
Abstract: 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 …

abstract arxiv convergence cs.lg denoising diffusion error gap insights mean novel paper practical square stat.ml strategy tasks type understanding utility