Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors

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.