Diffusion & Adversarial Schrödinger Bridges via Iterative Proportional Markovian Fitting

ICLR 2025 Conference Submission7648 Authors

Keywords: Schrödinger Bridge, Optimal Transport, Entropic Optimal Transport, Unpaired Learning

Abstract: The Iterative Markovian Fitting (IMF) procedure based on iterative reciprocal and Markovian projections has recently been proposed as a powerful method for solving the Schrödinger Bridge problem. However, it has been observed that for the practical implementation of this procedure, it is crucial to alternate between fitting a forward and backward time diffusion at each iteration. Such implementation is thought to be a practical heuristic, which is required to stabilize training and obtain good results in applications such as unpaired domain translation. In our work, we show that this heuristic closely connects with the pioneer approaches for the Schrödinger Bridge based on the Iterative Proportional Fitting (IPF) procedure. Namely, we find that the practical implementation of IMF is, in fact, a combination of IMF and IPF procedures, and we call this combination the Iterative Proportional Markovian Fitting (IPMF) procedure. We show both theoretically and practically that this combined IPMF procedure can converge under more general settings, thus, showing that the IPMF procedure opens a door towards developing a unified framework for solving Schrödinger Bridge problems.

Primary Area: generative models

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Submission Number: 7648