The Score Hamiltonian: Mapping Diffusion Models to Adiabatic Transport

• URL: http://arxiv.org/abs/2606.05217v1
• Date: Thu, 28 May 2026 18:39:52 GMT
• Title: The Score Hamiltonian: Mapping Diffusion Models to Adiabatic Transport
• Abstract summary: We show an exact correspondence between sampling with score-based diffusion models and adiabatic transport of ground states.<n>We find the fundamental limit of sampling is set by the ratio of squared score-matching error to Score Hamiltonian spectral gap.
• Score: 9.659199680879262
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We exhibit an exact correspondence between sampling with score-based diffusion models and adiabatic transport of ground states for a family of Schrödinger 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 Poincaré constant of the data density.

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