AI 中文总结
本文提出边界抵消的分数-哈密顿量采样方法，通过虚时薛定谔对应将分数学习误差转化为哈密顿扰动，利用Morita--Nishimori边界抵消提升采样精度，并经反向SDE基准验证。
AI 中文摘要
扩散采样可视为概率密度的虚时退火。通过正/反欧几里得薛定谔对，我们证明固定噪声漂移会强制反向分数项，且相同的对数力是超对称分数哈密顿量的单侧虚时反绝热连接。该对应关系将分数学习误差转化为哈密顿量扰动，并得出调度原则：若前$r$个终端导数消失，Morita--Nishimori边界抵消将残余Hellinger误差从$T^{-2}$抑制至$T^{-2r-2}$，直至达到分数或采样下限。包括二维学习分数测试在内的反向SDE基准验证了预测的改进。
英文摘要
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.
Comments4 pages, 2 figures
