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Preservation of Log-Concavity and Convergence of Wasserstein-Fisher-Rao Gradient Flows

arXiv · AI, language, vision and robotics · article · Sep 16, 2026 · UTC

We study the convergence of Wasserstein-Fisher-Rao (WFR) gradient flows for sampling from probability distributions known up to a normalisation constant. By combining Wasserstein transport with Fisher-Rao birth-death dynamics, WFR flows balance exploration and selection. These flows have been recognised as a promising mechanism to accelerate convergence beyond Langevin dynamics. We show that for a class of strongly log-concave target distributions satisfying additional curvature conditions, WFR flows preserve strong log-concavity, in contrast to Wasserstein flows which enjoy this property only

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