提出新方法提升扩散模型采样效率与稳定性。
Control Variate Score Matching for Diffusion Models
- 引入控制变量得分匹配，结合两种现有方法优势。
- 在低噪声和高噪声下均实现更低方差，提升采样精度。
- 适用于无数据训练和无需重训练的高效采样场景。
从非归一化概率密度中采样是计算与物理科学中的普遍挑战。扩散模型为此提供了强大生成框架，但其性能依赖于对扰动目标分布得分的精确估计。现有方法面临两难：去噪得分恒等式（DSI）需要数据样本，在低噪声时方差高；目标得分恒等式（TSI）依赖能量函数，在高噪声时方差发散。本文提出控制变量得分恒等式（CVSI），一种无偏估计器，具有解析最优、状态与时间相关的控制系数，理论上在全扩散过程中最小化方差。CVSI作为稳健的即插即用估计器，显著提升了无数据采样器学习和免训练扩散采样的性能与效率，且可扩展至复杂高维能量模型。
原文摘要 · Abstract (English)
Sampling from unnormalized probability densities is a pervasive challenge across the computational and physical sciences. Diffusion models provide a powerful generative framework for this task, but their success relies on accurately estimating the score of the perturbed target distribution. Current approaches face a dichotomy between two standard estimation methods: the Denoising Score Identity (DSI) requires data samples and exhibits high variance at low noise levels, whereas the Target Score Identity (TSI) relies on the energy function and suffers from diverging variance at high noise levels. In this work, we reconcile both approaches by introducing the Control Variate Score Identity (CVSI), an unbiased estimator with an analytically optimal, state- and time-dependent control coefficient that theoretically minimizes variance over the entire diffusion process. CVSI serves as a robust plug-in estimator that significantly enhances performance and efficiency in data-free sampler learning and training-free diffusion sampling. These gains scale to complex, high-dimensional energy-based models.
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