Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors

Yazid Janati El Idrissi, Alain Durmus, Eric Moulines, Jimmy Olsson

Abstract: Interest in the use of Denoising Diffusion Models (DDM) as priors for solving inverse Bayesian problems has recently increased significantly. However, sampling from the resulting posterior distribution poses a challenge. To solve this problem, previous works have proposed approximations to bias the drift term of the diffusion. In this work, we take a different approach and utilize the specific structure of the DDM prior to define a set of intermediate and simpler posterior sampling problems, resulting in a lower approximation error compared to previous methods. We empirically demonstrate the reconstruction capability of our method for general linear inverse problems using synthetic examples and various image restoration tasks.