[2601.06810] WFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transport

Computer Science > Machine Learning arXiv:2601.06810 (cs) [Submitted on 11 Jan 2026 (v1), last revised 2 Apr 2026 (this version, v2)] Title:WFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transport Authors:Qiangwei Peng, Zihan Wang, Junda Ying, Yuhao Sun, Qing Nie, Lei Zhang, Tiejun Li, Peijie Zhou View a PDF of the paper titled WFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transport, by Qiangwei Peng and 7 other authors View PDF HTML (experimental) Abstract:The Wasserstein-Fisher-Rao (WFR) metric extends dynamic optimal transport (OT) by coupling displacement with change of mass, providing a principled geometry for modeling unbalanced snapshot dynamics. Existing WFR solvers, however, are often unstable, computationally expensive, and difficult to scale. Here we introduce WFR Flow Matching (WFR-FM), a simulation-free training algorithm that unifies flow matching with dynamic unbalanced OT. Unlike classical flow matching which regresses only a transport vector field, WFR-FM simultaneously regresses a vector field for displacement and a scalar growth rate function for birth-death dynamics, yielding continuous flows under the WFR geometry. Theoretically, we show that minimizing the WFR-FM loss exactly recovers WFR geodesics. Empirically, WFR-FM yields more accurate and robust trajectory inference in single-cell biology, reconstructing consistent dynamics with proliferation and apoptosis, estimating time-varying growth fields, and applying to generative dynamics under ...