The score in diffusion models obeys viscous Burgers dynamics, with binary mode boundaries producing a universal tanh interfacial profile whose sharpening marks speciation transitions.
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An abstract perturbation theorem for Fredholm sections on compact zero sets that preserves existing transversality and supports cobordism arguments, shown via re-proof of Schwarz's theorem on Hamiltonian action functionals.
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Score Shocks: The Burgers Equation Structure of Diffusion Generative Models
The score in diffusion models obeys viscous Burgers dynamics, with binary mode boundaries producing a universal tanh interfacial profile whose sharpening marks speciation transitions.