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This paper establishes a theoretical bridge between diffusion sampling and imaginary-time quantum annealing, framing score-based learning errors as Hamiltonian perturbations within a supersymmetric framework. By applying Morita–Nishimori boundary cancellation principles, the authors demonstrate a method to significantly suppress residual Hellinger error in reverse stochastic differential equation benchmarks. The work advances the mathematical understanding of how quantum-inspired dynamics can optimize sampling schedules for complex probability densities.
Boundary-Cancelled Score-Hamiltonian Sampling
arXiv:2609.05904v1 Announce Type: new 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.
Abstract:Diffusion sampling can be viewed as imaginary-time annealing of probability densities. From a forward/backward Euclidean Schrödinger 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.
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)
arXiv:2609.05904 [quant-ph]
(or arXiv:2609.05904v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.05904 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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