Transport meets Variational Inference: Controlled Monte Carlo Diffusions

• URL: http://arxiv.org/abs/2307.01050v9
• Date: Wed, 3 Jul 2024 23:25:33 GMT
• Title: Transport meets Variational Inference: Controlled Monte Carlo Diffusions
• Authors: Francisco Vargas, Shreyas Padhy, Denis Blessing, Nikolas Nüsken,
• Abstract summary: We present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of the emphControlled Monte Carlo Diffusion sampler (CMCD) for Bayesian computation.
• Score: 5.5654189024307685
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Connecting optimal transport and variational inference, we present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of the \emph{Controlled Monte Carlo Diffusion} sampler (CMCD) for Bayesian computation, a score-based annealing technique that crucially adapts both forward and backward dynamics in a diffusion model. On the way, we clarify the relationship between the EM-algorithm and iterative proportional fitting (IPF) for Schr{\"o}dinger bridges, deriving as well a regularised objective that bypasses the iterative bottleneck of standard IPF-updates. Finally, we show that CMCD has a strong foundation in the Jarzinsky and Crooks identities from statistical physics, and that it convincingly outperforms competing approaches across a wide array of experiments.

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