[2509.26364] Data-to-Energy Stochastic Dynamics

Computer Science > Machine Learning arXiv:2509.26364 (cs) [Submitted on 30 Sep 2025 (v1), last revised 2 Mar 2026 (this version, v2)] Title:Data-to-Energy Stochastic Dynamics Authors:Kirill Tamogashev, Nikolay Malkin View a PDF of the paper titled Data-to-Energy Stochastic Dynamics, by Kirill Tamogashev and Nikolay Malkin View PDF HTML (experimental) Abstract:The Schrödinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport to the stochastic case, has received attention due to its connections to diffusion models and flow matching, as well as its applications in the natural sciences. However, all existing algorithms allow to infer such dynamics only for cases where samples from both distributions are available. In this paper, we propose the first general method for modelling Schrödinger bridges when one (or both) distributions are given by their unnormalised densities, with no access to data samples. Our algorithm relies on a generalisation of the iterative proportional fitting (IPF) procedure to the data-free case, inspired by recent developments in off-policy reinforcement learning for training of diffusion samplers. We demonstrate the efficacy of the proposed data-to-energy IPF on synthetic problems, finding that it can successfully learn transports between multimodal distributions. As a secondary cons...