Transport meets Variational Inference: Controlled Monte Carlo Diffusions
This work provides a systematic framework for sampling and generative modeling that addresses the problem of efficient Bayesian computation for practitioners in machine learning and statistics.
The authors developed a principled framework connecting optimal transport and variational inference for sampling and generative modeling, culminating in the Controlled Monte Carlo Diffusion (CMCD) sampler for Bayesian computation. They demonstrated that CMCD convincingly outperforms competing approaches across a wide array of experiments.
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{ö}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.