Monte Carlo guided Diffusion for Bayesian linear inverse problems

bd3dowling / diffusion-research

Meta/super repository encapsulating my research on diffusion models and inverse problems

GNU General Public License v3.0

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Monte Carlo guided Diffusion for Bayesian linear inverse problems #13

Closed bd3dowling closed 1 month ago

bd3dowling commented 1 month ago

Cardoso, Gabriel, et al. Monte Carlo Guided Diffusion for Bayesian Linear Inverse Problems. arXiv:2308.07983, arXiv, 25 Oct. 2023. arXiv.org, http://arxiv.org/abs/2308.07983.

bd3dowling commented 1 month ago

Code: https://github.com/gabrielvc/mcg_diff (very nice)

bd3dowling commented 1 month ago

Paste from obsidian:

Really difficult paper to read...
Kinda nice formulation of the in-painting problem... weird notation
GMM example; lovely formulation in B.3.1
2.3, I guess, is the key being the proposal (contrast with that in [[@wuPracticalAsymptoticallyExact2023]]).
Uses APF.
"MCGdiff weights the backward process by the density of the forward one conditioned on $y$, resulting in a natural and consistent algorithm."
No requirement of forward-backwards diffusion equivalence.