让分数模型能用马尔可夫链蒙特卡洛采样，突破传统方法局限。
Score-Based Metropolis-Hastings Algorithms
- 基于细致平衡条件设计新损失函数，估算采样接受概率。
- 可在重尾分布等复杂场景实现高效采样，性能优于未调整算法。
- 适合需要高精度采样的科研与工业应用，尤其擅长复杂分布建模。
本文提出一种将分数模型与马尔可夫链蒙特卡洛（Metropolis-Hastings）算法结合的新方法。传统分数驱动扩散模型虽能精准学习数据点的得分函数，却缺乏能量函数，导致无法使用带有接受步骤的马尔可夫链蒙特卡洛方法。因此，通常仅采用无调整的朗之万算法进行采样，限制了其他依赖接受函数的先进算法的应用。为此，我们引入一种基于细致平衡条件的新损失函数，使在已学习得分函数的基础上能够估计马尔可夫链蒙特卡洛的接受概率。实验表明，该方法在多种场景下均有效，包括从重尾分布中采样，显著提升了采样质量。
原文摘要 · Abstract (English)
In this paper, we introduce a new approach for integrating score-based models with the Metropolis-Hastings algorithm. While traditional score-based diffusion models excel in accurately learning the score function from data points, they lack an energy function, making the Metropolis-Hastings adjustment step inaccessible. Consequently, the unadjusted Langevin algorithm is often used for sampling using estimated score functions. The lack of an energy function then prevents the application of the Metropolis-adjusted Langevin algorithm and other Metropolis-Hastings methods, limiting the wealth of other algorithms developed that use acceptance functions. We address this limitation by introducing a new loss function based on the \emph{detailed balance condition}, allowing the estimation of the Metropolis-Hastings acceptance probabilities given a learned score function. We demonstrate the effectiveness of the proposed method for various scenarios, including sampling from heavy-tail distributions.
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