Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation

Fuente: arXiv
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Main Authors: Schwienhorst, Benedikt Lütke, Klein, Nadja, Lederer, Johannes
Format: Preprint
Published: 2026
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author Schwienhorst, Benedikt Lütke
Klein, Nadja
Lederer, Johannes
author_facet Schwienhorst, Benedikt Lütke
Klein, Nadja
Lederer, Johannes
contents Score matching is an alternative to maximum likelihood estimation when the normalizing constant is unknown or too costly to evaluate. However, vanilla score matching has shown to be inefficient relative to maximum likelihood estimation for multimodal distributions with well-separated modes, which are commonly encountered in practical applications. We compare a novel diffusion-based denoising score matching estimator (DDSME) to the vanilla score matching estimator (SME) in this scenario. In particular, we prove statistical guarantees for both estimators, showing that the error bound for the vanilla SME worsens when the separation between the modes increases, which can be avoided in case of the DDSME with suitable hyperparameter tuning. This provides a novel theoretical explanation for the superior behavior of diffusion-based score matching over the vanilla version.
format Preprint
id arxiv_https___arxiv_org_abs_2605_22950
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation
Schwienhorst, Benedikt Lütke
Klein, Nadja
Lederer, Johannes
Machine Learning
Statistics Theory
Methodology
Score matching is an alternative to maximum likelihood estimation when the normalizing constant is unknown or too costly to evaluate. However, vanilla score matching has shown to be inefficient relative to maximum likelihood estimation for multimodal distributions with well-separated modes, which are commonly encountered in practical applications. We compare a novel diffusion-based denoising score matching estimator (DDSME) to the vanilla score matching estimator (SME) in this scenario. In particular, we prove statistical guarantees for both estimators, showing that the error bound for the vanilla SME worsens when the separation between the modes increases, which can be avoided in case of the DDSME with suitable hyperparameter tuning. This provides a novel theoretical explanation for the superior behavior of diffusion-based score matching over the vanilla version.
title Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation
topic Machine Learning
Statistics Theory
Methodology
url https://arxiv.org/abs/2605.22950