Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo

TL;DR

This paper introduces DDSMC, a sequential Monte Carlo method leveraging decoupled diffusion for efficient Bayesian inverse problem solving, demonstrating accuracy and versatility across synthetic, biological, and image data.

Contribution

It presents a novel DDSMC algorithm that utilizes decoupled diffusion for linear-Gaussian inverse problems, enabling larger updates and extending to discrete data.

Findings

Effective on synthetic, protein, and image data

Asymptotically exact method

Extensible to discrete data

Abstract

A recent line of research has exploited pre-trained generative diffusion models as priors for solving Bayesian inverse problems. We contribute to this research direction by designing a sequential Monte Carlo method for linear-Gaussian inverse problems which builds on "decoupled diffusion", where the generative process is designed such that larger updates to the sample are possible. The method is asymptotically exact and we demonstrate the effectiveness of our Decoupled Diffusion Sequential Monte Carlo (DDSMC) algorithm on both synthetic as well as protein and image data. Further, we demonstrate how the approach can be extended to discrete data.