Variance-Reduced Diffusion Sampling via Target Score Identity

Alois Duston; Tan Bui-Thanh

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arXiv · 2601.01594

Variance-Reduced Diffusion Sampling via Target Score Identity

Alois Duston·Tan Bui-Thanh

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Abstract

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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Alois Duston, Tan Bui-Thanh. 2026-01-04. Variance-Reduced Diffusion Sampling via Target Score Identity. https://arxiv.org/abs/2601.01594

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