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This paper reveals that diffusion models and flow matching are two sides of the same Wasserstein geometry: diffusion follows a free-energy gradient flow (initial-value problem), while flow matching follows a Wasserstein geodesic (boundary-value problem), and they are unified through the JKO scheme.
Introduces QuantFPFlow, a reinforcement learning framework that uses quantum amplitude estimation to achieve a quadratic speedup in estimating the Fokker-Planck partition function for continuous control, improving exploration and avoiding local optima.