[2410.02601] Diffusion & Adversarial Schrödinger Bridges via Iterative Proportional Markovian Fitting

Computer Science > Machine Learning arXiv:2410.02601 (cs) [Submitted on 3 Oct 2024 (v1), last revised 3 Mar 2026 (this version, v5)] Title:Diffusion & Adversarial Schrödinger Bridges via Iterative Proportional Markovian Fitting Authors:Sergei Kholkin, Grigoriy Ksenofontov, David Li, Nikita Kornilov, Nikita Gushchin, Alexandra Suvorikova, Alexey Kroshnin, Evgeny Burnaev, Alexander Korotin View a PDF of the paper titled Diffusion & Adversarial Schr\"odinger Bridges via Iterative Proportional Markovian Fitting, by Sergei Kholkin and 8 other authors View PDF HTML (experimental) 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 F...