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Riemannian Neural Hamiltonian Flows: Geodesic Symplectic Transport and Interpretability

arXiv · AI, language, vision and robotics · article · Sep 18, 2026 · UTC

Hamiltonian normalizing flows are attractive generative models because their phase-space maps are invertible and volume preserving, but most neural constructions are formulated in Euclidean space. We introduce Riemannian Neural Hamiltonian Flows, which combine the fixed kinetic energy of a Riemannian manifold, a learned scalar potential, and an explicit geodesic leapfrog integrator. Our analysis explains how the learned Hamiltonian can be made interpretable. Every normalizable potential defines an implicit profile, and the position marginal initially accelerates along the relative score betwee

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