AI Insight
This paper introduces a new method for learning dynamic transport maps between distributions when intermediate observed data points are available. The authors extend flow matching by incorporating optimal transport potentials that guide the flows through intermediate marginal distributions, creating a simulation-free algorithm called OTP-FM. The method demonstrates improved performance and training efficiency on biological, oceanographic, and meteorological datasets compared to existing approaches.
Why it matters
The technique addresses a critical gap in modeling temporal evolution of dynamical systems across scientific domains where sequential snapshots of data are available, such as tracking cell development over time or predicting weather patterns. By efficiently incorporating intermediate observations, this method could improve predictions in fields ranging from developmental biology to climate science.
Understand the Science
arXiv:2606.05327v1 Announce Type: cross
Abstract: Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions. However, less explored is the setting with intermediate observed marginals that can help constrain the flows between the endpoints. This “multimarginal” regime is central to modeling temporal evolution in dynamical systems in many scientific domains that can sample sequential distributions. We tackle this problem with a novel approach that leverages the connection between FM and dynamic optimal transport (OT), softly steering the flow towards the intermediate marginals through potential terms in the dynamic OT action. By extending the conditional FM learning target to incorporate these potentials, we derive an efficient, simulation-free algorithm for multimarginal FM that offers considerable flexibility in the spatiotemporal dynamics of the learned flows. We demonstrate state-of-the-art performance and training efficiency of OT-potential FM (OTP-FM) on diverse single-cell RNA sequencing, oceanographic, and meteorological datasets. Our code is available at https://github.com/Bexorg-Inc/OTP-FM.
Source: Multimarginal flow matching with optimal transport potentials