The Score Hamiltonian: Mapping Diffusion Models to Adiabatic Transport
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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 Schr\"odinger 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...
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 Schr\"odinger 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...