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[2602.22265] Entropy-Controlled Flow Matching
Summary
The paper introduces Entropy-Controlled Flow Matching (ECFM), a method that optimizes flow matching in machine learning by controlling information geometry and entropy rates, enhancing performance in generative models.
Why It Matters
ECFM addresses limitations in current flow-matching techniques by enforcing entropy constraints, which can lead to improved model stability and performance in generative tasks. This is particularly relevant for applications in machine learning and computer vision where data representation is critical.
Key Takeaways
- ECFM introduces a constrained variational principle to control entropy in flow matching.
- The method enhances stability and performance of generative models by addressing low-entropy bottlenecks.
- ECFM is mathematically grounded in convex optimization and Wasserstein space.
- The approach provides guarantees for mode coverage and density stability.
- ECFM recovers classical optimal transport in specific conditions, bridging modern and traditional methods.
Computer Science > Machine Learning arXiv:2602.22265 (cs) [Submitted on 25 Feb 2026] Title:Entropy-Controlled Flow Matching Authors:Chika Maduabuchi View a PDF of the paper titled Entropy-Controlled Flow Matching, by Chika Maduabuchi View PDF 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. Subjects: Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV) Cite as: arXiv:2602.22265 [cs.LG] (or arXiv:2602.22265v1 [cs.LG] for this version...
