首次为随机定位采样算法提供总变差误差保证，证明其在高维下高效收敛。
Total Variation Guarantees for Sampling with Stochastic Localization
- 基于随机定位思想设计采样算法，结合得分模型理论分析
- 在目标分布满足最小假设下，达到ε精度所需步数与维度线性相关（含对数因子）
- 揭示离散化点选择的最优性，适合关注生成模型理论保障的研究者
受得分生成模型成功启发，近年涌现出多种基于扩散的采样算法，用于从可访问未归一化密度的概率测度中采样。其中，Grenioux 等人提出的 SLIPS 算法基于随机定位，虽具强经验性能，但此前缺乏严格收敛分析。本文首次为 SLIPS 提供了总变差距离下的收敛保证。在对目标分布最弱假设下，我们的界表明：达到 ε 精度所需的迭代步数随维度线性增长，仅含对数因子。分析结合得分生成模型理论，并进一步解释了实验中观察到的最优离散化点选择机制。
原文摘要 · Abstract (English)
Motivated by the success of score-based generative models, a number of diffusion-based algorithms have recently been proposed for the problem of sampling from a probability measure whose unnormalized density can be accessed. Among them, Grenioux et al. introduced SLIPS, a sampling algorithm based on Stochastic Localization. While SLIPS exhibits strong empirical performance, no rigorous convergence analysis has previously been provided. In this work, we close this gap by establishing the first guarantee for SLIPS in total variation distance. Under minimal assumptions on the target, our bound implies that the number of steps required to achieve an $\varepsilon$-guarantee scales linearly with the dimension, up to logarithmic factors. The analysis leverages techniques from the theory of score-based generative models and further provides theoretical insights into the empirically observed optimal choice of discretization points.
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