The Score Hamiltonian: Mapping Diffusion Models to Adiabatic Transport

arXiv:2606.05217v1 Announce Type: cross Abstract: We exhibit an exact correspondence between sampling with score-based diffusion models and adiabatic transport of ground states for a family of Schrodinger operators we call Score Hamiltonians, built from the learned score's quantum potential. We obtain novel density reconstruction bounds and principled annealing schedules via adiabatic theorems for Fokker-Planck equations with time-varying potentials. We find the fundamental limit of sampling is set by the ratio of squared score-matching error to Score Hamiltonian spectral gap - the inverse Poincare constant of the data density.

Source: arXiv cs.AI | 2026-06-06