Boundary-Cancelled Score-Hamiltonian Sampling

Abstract

Diffusion sampling can be viewed as imaginary-time annealing of probability densities. From a forward/backward Euclidean Schr\"odinger pair, we show that fixing the noising drift forces the reverse score term, and that the same logarithmic force is the one-sided imaginary-time counterdiabatic connection of a supersymmetric Score Hamiltonian. The correspondence turns score-learning error into a Hamiltonian perturbation and yields a schedule principle: if the first $r$ terminal derivatives vanish, Morita--Nishimori boundary cancellation suppresses the residual Hellinger error from $T^{-2}$ to $T^{-2r-2}$ until score or sampling floors are reached. Reverse-SDE benchmarks, including two-dimensional learned-score tests, confirm the predicted improvement.