@inproceedings{
brekelmans2023on,
title={On Schr\"odinger Bridge Matching and Expectation Maximization},
author={Rob Brekelmans and Kirill Neklyudov},
booktitle={NeurIPS 2023 Workshop Optimal Transport and Machine Learning},
year={2023},
url={https://openreview.net/forum?id=Bd4DTPzOGO}
}
In this work, we analyze methods for solving the Schrödinger Bridge problem from the perspective of alternating KL divergence minimization.  While existing methods such as Iterative Proportional- or Markovian- Fitting require exact updates due to each iteration optimizing the same argument in the \kl divergence, we justify a joint optimization of a single KL divergence objective from the perspective of information geometry.  As in the variational EM algorithm, this allows for partial, stochastic gradient updates to decrease a unified objective.  We highlight connections with related bridge-matching, flow-matching, and few-step generative modeling approaches, where various parameterizations of the coupling distributions are contextualized from the perspective of marginal-preserving inference.
On Schrödinger Bridge Matching and Expectation Maximization
Rob Brekelmans Kirill Neklyudov