扩散去噪得分匹配在多峰分布中比传统方法更准，理论证明其误差不随峰间距增大而恶化。
Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation
- 用扩散模型去噪方式改进得分匹配估计，提升多峰分布拟合能力
- 理论证明传统方法误差随峰间距增大而上升，新方法可避免此问题
- 适合研究生成模型、统计推断的学者参考，尤其关注多峰数据建模
当归一化常数未知或计算成本过高时，得分匹配是最大似然估计的替代方法。然而，对于具有明显分离模式的多峰分布（实际应用中常见），传统得分匹配（SME）表现出效率低下。本文比较了一种新型基于扩散的去噪得分匹配估计器（DDSME）与传统得分匹配估计器（SME）。我们为两者提供了统计保证，证明当模式间分离度增加时，传统SME的误差界会变差，而通过适当超参数调优，DDSME可避免该问题。这为扩散型得分匹配优于传统方法提供了新的理论解释。数值实验验证了上述理论发现。
原文摘要 · Abstract (English)
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. We support our theoretical findings by numerical experiments.
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