Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo
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.
Cite
@article{arxiv.2502.06379,
title = {Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo},
author = {Filip Ekström Kelvinius and Zheng Zhao and Fredrik Lindsten},
journal= {arXiv preprint arXiv:2502.06379},
year = {2025}
}
Comments
Accepted to ICML 2025, official PMLR proceedings can be found at https://proceedings.mlr.press/v267/ekstrom-kelvinius25b.html. Code available at https://github.com/filipekstrm/ddsmc