Bridging diffusion posterior sampling and Monte Carlo methods: a survey
Janati, Yazid Moulines, Eric Olsson, Jimmy Oliviero-Durmus, Alain
Janati, Yazid
Moulines, Eric
Olsson, Jimmy
Oliviero-Durmus, Alain
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Machine Learning
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Journal article
Date
2025
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English
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Abstract
Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modelling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by serving as priors. This review offers a comprehensive overview of current methods that leverage pre-trained diffusion models alongside Monte Carlo methods to address Bayesian inverse problems without requiring additional training. We show that these methods primarily employ a twisting mechanism for the intermediate distributions within the diffusion process, guiding the simulations towards the posterior distribution. We describe how various Monte Carlo methods are then used to aid in sampling from these twisted distributions.
Citation
Y. Janati, E. Moulines, J. Olsson, and A. Oliviero-Durmus, “Bridging diffusion posterior sampling and Monte Carlo methods: a survey,” Philosophical Transactions A, 2025, doi: 10.1098/RSTA.2024.0331
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Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Conference
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The Royal Society