Transport Meets Variational Inference: Controlled Monte Carlo Diffusions

TY - CHAP

T1 - Transport Meets Variational Inference: Controlled Monte Carlo Diffusions

AU - Vargas, Francisco

AU - Padhy, Shreyas

AU - Blessing, Denis

AU - Nusken, Nikolas

PY - 2024/5/7

Y1 - 2024/5/7

N2 - 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 Controlled Monte Carlo Diffusions for sampling and inference, a score-based annealing tech- nique 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 Schro ̈dinger bridges, providing a conceptual link between fields. 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.

AB - 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 Controlled Monte Carlo Diffusions for sampling and inference, a score-based annealing tech- nique 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 Schro ̈dinger bridges, providing a conceptual link between fields. 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.

M3 - Conference paper

BT - The Twelfth International Conference on Learning Representations

ER -