Contractive Diffusion Probabilistic Models
Wenpin Tang, Hanyang Zhao · SIAM Journal on Imaging Sciences · 2026
Abstract. Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed score matching, we propose a new criterion—the contraction property of backward sampling in the design of DPMs, leading to a novel class of contractive DPMs (CDPMs). Our key insight is that the contraction property can provably narrow score-matching errors and discretization errors; thus our proposed CDPMs are robust to both sources of error. For practical use, we showcase that CDPM can leverage weights of pretrained DPMs by a simple transformation, without the necessity of further training. We corroborated our approach by experiments on Swiss Roll, MNIST, CIFAR-10 32[Formula: see text]32, and AFHQ 64[Formula: see text]64 dataset. Notably, CDPM steadily improves the performance of baseline score-based diffusion models.