Monte Carlo guided Diffusion for Bayesian linear inverse problems | Vidéo | Carmin.tv

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Monte Carlo guided Diffusion for Bayesian linear inverse problems

By Sylvain Le Corff

Appears in collection : Autumn school in Bayesian Statistics / École d'automne en statistique bayésienne

Ill-posed linear inverse problems that combine knowledge of the forward measurement model with prior models arise frequently in various applications, from computational photography to medical imaging. Recent research has focused on solving these problems with score-based generative models (SGMs) that produce perceptually plausible images, especially in inpainting problems. In this study, we exploit the particular structure of the prior defined in the SGM to formulate recovery in a Bayesian framework as a Feynman–Kac model adapted from the forward diffusion model used to construct score-based diffusion. To solve this Feynman–Kac problem, we propose the use of Sequential Monte Carlo methods. The proposed algorithm, MCGdiff, is shown to be theoretically grounded and we provide numerical simulations showing that it outperforms competing baselines when dealing with ill-posed inverse problems.

Information about the video

Date of recording 31/10/2023
Date of publication 27/11/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20107003
Cite this video Le Corff, Sylvain (31/10/2023). Monte Carlo guided Diffusion for Bayesian linear inverse problems. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20107003
URL https://dx.doi.org/10.24350/CIRM.V.20107003

Domain(s)

Bibliography

CARDOSO, Gabriel, IDRISSI, Yazid Janati El, CORFF, Sylvain Le, et al. Monte Carlo guided Diffusion for Bayesian linear inverse problems. arXiv preprint arXiv:2308.07983, 2023. - https://arxiv.org/abs/2308.07983

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