Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
Yazid Janati Alain Durmus Eric Moulines Jimmy Olsson
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.