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Symplectic Manifold Geometry and Hamiltonian Score Dynamics in Multi-Modal Video Generation1. 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,...0 Commentaires 0 Parts 79 Vue 0 Aperçu
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Differential Geometry and Continuous Spatio-Temporal Flows in Generative Video Architectures1. Topological Formulations in Continuous Latent Video Dynamics The progression of synthetic media systems from frame-by-frame interpolation to continuous generative spacetime marks an essential inflection point in digital visual computing. Early deep learning video systems suffered from temporal flickering, spatial degradation, and structural incoherence because they modeled time as discrete...0 Commentaires 0 Parts 136 Vue 0 Aperçu