Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
This work addresses a bottleneck in applying diffusion models to inverse problems, offering a more accurate and versatile sampling method for researchers in computational imaging and related fields, though it appears incremental as it builds on existing DDM priors.
The paper tackles the challenge of sampling from complex posterior distributions in Bayesian inverse problems using denoising diffusion priors, presenting a divide-and-conquer framework that reduces approximation error without retraining and demonstrates effectiveness across various problems.
Recent advancements in solving Bayesian inverse problems have spotlighted denoising diffusion models (DDMs) as effective priors. Although these have great potential, DDM priors yield complex posterior distributions that are challenging to sample. Existing approaches to posterior sampling in this context address this problem either by retraining model-specific components, leading to stiff and cumbersome methods, or by introducing approximations with uncontrolled errors that affect the accuracy of the produced samples. We present an innovative framework, divide-and-conquer posterior sampling, which leverages the inherent structure of DDMs to construct a sequence of intermediate posteriors that guide the produced samples to the target posterior. Our method significantly reduces the approximation error associated with current techniques without the need for retraining. We demonstrate the versatility and effectiveness of our approach for a wide range of Bayesian inverse problems. The code is available at \url{https://github.com/Badr-MOUFAD/dcps}