Entropy-Controlled Flow Matching

• URL: http://arxiv.org/abs/2602.22265v1
• Date: Wed, 25 Feb 2026 06:07:01 GMT
• Title: Entropy-Controlled Flow Matching
• Authors: Chika Maduabuchi,
• Abstract summary: We propose a constrained variational principle over continuity-equation paths enforcing a global entropy-rate budget d/dt H(mu_t) >= -lambda.<n>We obtain certificate-style mode-coverage and density-floor guarantees with Lipschitz, and construct near-optimal counterexamples for unconstrained flow matching.
• Score: 0.08460698440162889
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Modern vision generators transport a base distribution to data through time-indexed measures, implemented as deterministic flows (ODEs) or stochastic diffusions (SDEs). Despite strong empirical performance, standard flow-matching objectives do not directly control the information geometry of the trajectory, allowing low-entropy bottlenecks that can transiently deplete semantic modes. We propose Entropy-Controlled Flow Matching (ECFM): a constrained variational principle over continuity-equation paths enforcing a global entropy-rate budget d/dt H(mu_t) >= -lambda. ECFM is a convex optimization in Wasserstein space with a KKT/Pontryagin system, and admits a stochastic-control representation equivalent to a Schrodinger bridge with an explicit entropy multiplier. In the pure transport regime, ECFM recovers entropic OT geodesics and Gamma-converges to classical OT as lambda -> 0. We further obtain certificate-style mode-coverage and density-floor guarantees with Lipschitz stability, and construct near-optimal collapse counterexamples for unconstrained flow matching.

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