Variance-Reduced Diffusion Sampling via Target Score Identity
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| Format: | Preprint |
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2026
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| _version_ | 1866915749260427264 |
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| author | Duston, Alois Bui-Thanh, Tan |
| author_facet | Duston, Alois Bui-Thanh, Tan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_01594 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Variance-Reduced Diffusion Sampling via Target Score Identity Duston, Alois Bui-Thanh, Tan Machine Learning 68T07, 65C05, 60J60, 62F15 G.3; I.2.6; I.5.1 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. |
| title | Variance-Reduced Diffusion Sampling via Target Score Identity |
| topic | Machine Learning 68T07, 65C05, 60J60, 62F15 G.3; I.2.6; I.5.1 |
| url | https://arxiv.org/abs/2601.01594 |