用分数驱动的流模型实现高效无归一化采样
SCORENF: Score-based Normalizing Flows for Sampling Unnormalized distributions
- 结合分数学习与归一化流，加独立马尔可夫链蒙特卡洛模块
- 小样本训练下仍保持高采样效率，避免模式覆盖与坍塌
- 适合物理模拟等需精准采样的高维无归一化分布场景
无归一化概率分布是建模复杂物理系统的核心。传统蒙特卡洛方法（MCMC）常面临收敛慢、临界减速、模式混合差、自相关高等问题。而基于似然和对抗学习的模型虽有效，却高度依赖大数据，易出现模式覆盖或坍塌。本文提出ScoreNF——一种基于归一化流架构、融合独立马尔可夫链蒙特卡洛（IMH）模块的分数学习框架，可高效无偏地从无归一化目标分布中采样。实验表明，ScoreNF在小规模训练集下仍具高性能，降低对昂贵MCMC数据的依赖。我们还提出评估模式覆盖与坍塌行为的方法。在二维合成分布（MOG-4 和 MOG-8）及高维 $ϕ^4$ 格点场论分布上验证了其有效性。
原文摘要 · Abstract (English)
Unnormalized probability distributions are central to modeling complex physical systems across various scientific domains. Traditional sampling methods, such as Markov Chain Monte Carlo (MCMC), often suffer from slow convergence, critical slowing down, poor mode mixing, and high autocorrelation. In contrast, likelihood-based and adversarial machine learning models, though effective, are heavily data-driven, requiring large datasets and often encountering mode covering and mode collapse. In this work, we propose ScoreNF, a score-based learning framework built on the Normalizing Flow (NF) architecture, integrated with an Independent Metropolis-Hastings (IMH) module, enabling efficient and unbiased sampling from unnormalized target distributions. We show that ScoreNF maintains high performance even with small training ensembles, thereby reducing reliance on computationally expensive MCMC-generated training data. We also present a method for assessing mode-covering and mode-collapse behaviours. We validate our method on synthetic 2D distributions (MOG-4 and MOG-8) and the high-dimensional $ϕ^4$ lattice field theory distribution, demonstrating its effectiveness for sampling tasks.
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