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
Text
Ekström Kelvinius et al. "Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo." Proceedings of the 42nd International Conference on Machine Learning, 2025.Markdown
[Ekström Kelvinius et al. "Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo." Proceedings of the 42nd International Conference on Machine Learning, 2025.](https://mlanthology.org/icml/2025/ekstromkelvinius2025icml-solving/)BibTeX
@inproceedings{ekstromkelvinius2025icml-solving,
title = {{Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo}},
author = {Ekström Kelvinius, Filip and Zhao, Zheng and Lindsten, Fredrik},
booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
year = {2025},
pages = {15148-15181},
volume = {267},
url = {https://mlanthology.org/icml/2025/ekstromkelvinius2025icml-solving/}
}