Control Variate Score Matching for Diffusion Models

Fuente: arXiv
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Autores principales: Kahouli, Khaled, Elie, Romuald, Müller, Klaus-Robert, Berthet, Quentin, Unke, Oliver T., Doucet, Arnaud
Formato: Preprint
Publicado: 2025
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author Kahouli, Khaled
Elie, Romuald
Müller, Klaus-Robert
Berthet, Quentin
Unke, Oliver T.
Doucet, Arnaud
author_facet Kahouli, Khaled
Elie, Romuald
Müller, Klaus-Robert
Berthet, Quentin
Unke, Oliver T.
Doucet, Arnaud
contents Diffusion models offer a robust framework for sampling from unnormalized probability densities, which requires accurately estimating the score of the noise-perturbed target distribution. While the standard Denoising Score Identity (DSI) relies on data samples, access to the target energy function enables an alternative formulation via the Target Score Identity (TSI). However, these estimators face a fundamental variance trade-off: DSI exhibits high variance in low-noise regimes, whereas TSI suffers from high variance at high noise levels. In this work, we reconcile these approaches by unifying both estimators within the principled framework of control variates. We introduce the Control Variate Score Identity (CVSI), deriving an optimal, time-dependent control coefficient that theoretically guarantees variance minimization across the entire noise spectrum. We demonstrate that CVSI serves as a robust, low-variance plug-in estimator that significantly enhances sample efficiency in both data-free sampler learning and inference-time diffusion sampling.
format Preprint
id arxiv_https___arxiv_org_abs_2512_20003
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Control Variate Score Matching for Diffusion Models
Kahouli, Khaled
Elie, Romuald
Müller, Klaus-Robert
Berthet, Quentin
Unke, Oliver T.
Doucet, Arnaud
Machine Learning
Diffusion models offer a robust framework for sampling from unnormalized probability densities, which requires accurately estimating the score of the noise-perturbed target distribution. While the standard Denoising Score Identity (DSI) relies on data samples, access to the target energy function enables an alternative formulation via the Target Score Identity (TSI). However, these estimators face a fundamental variance trade-off: DSI exhibits high variance in low-noise regimes, whereas TSI suffers from high variance at high noise levels. In this work, we reconcile these approaches by unifying both estimators within the principled framework of control variates. We introduce the Control Variate Score Identity (CVSI), deriving an optimal, time-dependent control coefficient that theoretically guarantees variance minimization across the entire noise spectrum. We demonstrate that CVSI serves as a robust, low-variance plug-in estimator that significantly enhances sample efficiency in both data-free sampler learning and inference-time diffusion sampling.
title Control Variate Score Matching for Diffusion Models
topic Machine Learning
url https://arxiv.org/abs/2512.20003