Abstract
The Iterative Markovian Fitting (IMF) procedure, which iteratively projects onto the space of Markov processes and their reciprocal class, successfully solves the Schrödinger Bridge problem. However, an efficient practical implementation requires a heuristic modification - alternating between fitting forward and backward time diffusion at each iteration. This modification is crucial for stabilizing training and achieving reliable results in applications such as unpaired domain translation. Our work reveals a close connection between the modified version of IMF and the Iterative Proportional Fitting (IPF) procedure - a foundational method for the Schrödinger Bridge problem, also known as Sinkhorn’s algorithm. Specifically, we demonstrate that this heuristic modification of the IMF effectively integrates both IMF and IPF procedures. We refer to this combined approach as the Iterative Proportional Markovian Fitting (IPMF) procedure. Through theoretical and empirical analysis, we establish the convergence of IPMF procedure under various settings, contributing to developing a unified framework for solving Schrödinger Bridge problems.
Alexander Korotin
Assistant professor,
senior research scientist
My research interests include generative modeling, unpaired learning, optimal transport and Schrodinger bridges.