Diffusion & Adversarial Schrödinger Bridges via Iterative Proportional Markovian Fitting
Sergei Kholkin, Grigoriy Ksenofontov, David Li, Nikita Maksimovich Kornilov, Nikita Gushchin, Alexandra Suvorikova, Alexey Kroshnin, Evgeny Burnaev
Abstract
The Iterative Markovian Fitting (IMF) procedure, which iteratively projects onto the space of Markov processes and the reciprocal class, successfully solves the Schrödinger Bridge (SB) 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 SB problem, also known as Sinkhorn’s algorithm. Specifically, we demonstrate that the 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 the IPMF procedure under various settings, contributing to developing a unified framework for solving SB problems. Moreover, from a practical standpoint, the IPMF procedure enables a flexible trade-off between image similarity and generation quality, offering a new mechanism for tailoring models to specific tasks.
BibTeX
@inproceedings{
kholkin2026diffusion,
title={Diffusion \& Adversarial Schr\"odinger Bridges via Iterative Proportional Markovian Fitting},
author={Sergei Kholkin and Grigoriy Ksenofontov and David Li and Nikita Maksimovich Kornilov and Nikita Gushchin and Alexandra Suvorikova and Alexey Kroshnin and Evgeny Burnaev and Alexander Korotin},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=38fGCBhFF5}
}