Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors

TL;DR

This paper introduces a divide-and-conquer approach for sampling from complex posteriors in denoising diffusion models, improving accuracy without retraining, and demonstrating effectiveness across various inverse problems.

Contribution

We propose a novel divide-and-conquer posterior sampling framework that leverages DDM structure to reduce approximation errors without retraining.

Findings

Significantly reduces sampling approximation errors.

Applicable to a wide range of Bayesian inverse problems.

No need for retraining model components.

Abstract

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}