We study variance reduction for score estimation and diffusion-based sampling in settings where the clean (target) score is available or can be approximated. Starting from the Target Score Identity (TSI), which expresses the noisy marginal score as a conditional expectation of the target score under the forward diffusion, we develop: (i) a plug-and-play nonparametric self-normalized importance sampling estimator compatible with standard reverse-time solvers, (ii) a variance-minimizing \emph{state- and time-dependent} blending rule between Tweedie-type and TSI estimators together with an anti-correlation analysis, (iii) a data-only extension based on locally fitted proxy scores, and (iv) a likelihood-tilting extension to Bayesian inverse problems. We also propose a \emph{Critic--Gate} distillation scheme that amortizes the state-dependent blending coefficient into a neural gate. Experiments on synthetic targets and PDE-governed inverse problems demonstrate improved sample quality for a fixed simulation budget.

翻译：本研究探讨在可获得或可近似干净（目标）分数的情况下，分数估计与基于扩散的采样中的方差缩减问题。从目标分数恒等式（TSI）出发——该恒等式将含噪边缘分数表达为前向扩散下目标分数的条件期望——我们发展了：（i）一种即插即用的非参数化自归一化重要性采样估计器，兼容标准逆时求解器；（ii）一种方差最小化的、状态与时间依赖的Tweedie型与TSI估计器混合规则，并附有抗相关性分析；（iii）一种基于局部拟合代理分数的纯数据扩展方法；（iv）一种适用于贝叶斯逆问题的似然倾斜扩展。我们还提出了一种Critic–Gate蒸馏方案，将状态依赖的混合系数摊销至一个神经门中。在合成目标与偏微分方程约束的逆问题上的实验表明，在固定仿真预算下，采样质量得到了提升。