Symplectic Manifold Geometry and Hamiltonian Score Dynamics in...

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2026-09-20 03:13:06 -

Symplectic Manifold Geometry and Hamiltonian Score Dynamics in Multi-Modal Video Generation

1. Beyond Dissipative Diffusion: The Geometric Imperative for Hamiltonian Systems First-generation continuous diffusion models approached video synthesis through the mathematical lens of dissipative Fokker-Planck equations and overdamped Langevin dynamics. While mathematically tractable for static image frames, unconstrained dissipative flows introduce severe gradient damping, mode collapse,...

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