Reminder - December 12, with Sylvain Le Corff

[All About That Bayes]

Dear all,

A gentle reminder about this afternoon session at 16:00. Sylvain Le Corff (LPSM, Sorbonne Université) will give a talk on Monte Carlo guided diffusions for Bayesian inverse problems.

Note that the room has changed for this session, the seminar will take place in room 15-16-201, Sorbonne Université, Campus Pierre et Marie Curie, (between towers 15 and 16, second floor, room 201) and will be available online via zoom: https://cnrs.zoom.us/j/99452802078?pwd=aWV1V3cyYzB3cHl5emY3a0ZKczNuQT09
(ID de réunion: 994 5280 2078, Code secret: ic51nf)


Best regards,
The All about that Bayes organising team

Monte Carlo guided Diffusion for Bayesian linear inverse problems
Joint work with G. Cardoso, Y. Janati and E. Moulines

Abstract: 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.