@inproceedings{
janati2024divideandconquer,
title={Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors},
author={Yazid Janati and Badr MOUFAD and Alain Oliviero Durmus and Eric Moulines and Jimmy Olsson},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=BOrut7M2X7}
}
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 from.
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}
Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors
Yazid Janati Badr MOUFAD Alain Oliviero Durmus Eric Moulines Jimmy Olsson