提出新方法降低扩散模型采样方差，提升生成质量。
Variance-Reduced Diffusion Sampling via Target Score Identity
- 基于目标得分恒等式，设计无参数重要性采样估计器。
- 通过状态与时间相关混合规则，显著减少采样方差。
- 适用于物理建模和贝叶斯反问题，适合高精度生成场景。
我们研究在可获取或可近似清洁（目标）得分的场景下，得分估计与基于扩散的采样中的方差缩减问题。从目标得分恒等式（TSI）出发，该恒等式将噪声边际得分表示为前向扩散下目标得分的条件期望，我们提出了：(i) 一种可直接集成到标准逆时序求解器的非参数自归一化重要性采样估计器；(ii) 一种在状态与时间上依赖的、最小化方差的Tweedie型与TSI估计器混合规则，并附带反相关分析；(iii) 基于局部拟合代理得分的数据仅扩展；(iv) 针对贝叶斯反问题的似然倾斜扩展。此外，我们提出一种'批评者-门控'蒸馏方案，将状态依赖的混合系数摊销为神经门控。在合成目标和由偏微分方程控制的反问题上的实验表明，在固定模拟预算下，样本质量得到提升。
原文摘要 · Abstract (English)
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.
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