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

2026-05-21

AI Summary

This work addresses the degraded performance of conventional score matching in parameter estimation for multimodal distributions with well-separated modes. To overcome this limitation, the authors propose the Diffusion Denoising Score Matching Estimator (DDSME), which integrates diffusion models with denoising score matching to substantially improve estimation efficiency in such settings. Theoretical analysis establishes, for the first time, that DDSME maintains a stable error bound even as mode separation increases, whereas the error of traditional score matching deteriorates sharply. By deriving and comparing the error bounds of DDSME and conventional score matching, this study rigorously demonstrates the statistical superiority of DDSME in multimodal scenarios.

Abstract

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.

Problem

• score matching
• multimodal distributions
• parameter estimation
• diffusion-based denoising
• statistical efficiency

Innovation

• diffusion-based denoising
• score matching
• multimodal distributions
• statistical guarantees
• parameter estimation