Score Shocks: The Burgers Equation Structure of Diffusion Generative Models
We analyze the score field of a diffusion generative model through a Burgers-type evolution law. For VE diffusion, the heat-evolved data density implies that the score obeys viscous Burgers in one dimension and the corresponding irrotational vector Burgers system in $\R^d$, giving a PDE view of \emph{speciation transitions} as the sharpening of inter-mode interfaces. For any binary decomposition of the noised density into two positive heat solutions, the score separates into a smooth background and a universal $\tanh$ interfacial term determined by the component log-ratio; near a regular binary mode boundary this yields a normal criterion for speciation. In symmetric binary Gaussian mixtu...
| Authors | Krisanu Sarkar |
|---|---|
| Primary category | cond-mat.stat-mech |
| Published | 8 April 2026 |
| Last updated at source | 8 April 2026 |
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