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

Filip Ekström Kelvinius, Zheng Zhao, Fredrik Lindsten
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:15148-15181, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v267-ekstrom-kelvinius25b, title = {Solving Linear-{G}aussian {B}ayesian Inverse Problems with Decoupled Diffusion Sequential {M}onte {C}arlo}, author = {Ekstr\"{o}m Kelvinius, Filip and Zhao, Zheng and Lindsten, Fredrik}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {15148--15181}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/ekstrom-kelvinius25b/ekstrom-kelvinius25b.pdf}, url = {https://proceedings.mlr.press/v267/ekstrom-kelvinius25b.html}, 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.} }
Endnote
%0 Conference Paper %T Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo %A Filip Ekström Kelvinius %A Zheng Zhao %A Fredrik Lindsten %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-ekstrom-kelvinius25b %I PMLR %P 15148--15181 %U https://proceedings.mlr.press/v267/ekstrom-kelvinius25b.html %V 267 %X 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.
APA
Ekström Kelvinius, F., Zhao, Z. & Lindsten, F.. (2025). Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:15148-15181 Available from https://proceedings.mlr.press/v267/ekstrom-kelvinius25b.html.

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