用朗之万采样器高效生成复杂分布样本，提升概率流ODE采样精度。
Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEs
- 基于线性随机插值构造概率流ODE，用朗之万采样器模拟中间分布。
- 在多模态分布上实现高效采样，支持高维数据与贝叶斯推断任务。
- 提供收敛性理论保证，适合需高精度采样的机器学习研究者。
我们提出一种基于线性随机插值导出的概率流常微分方程（ODE）的新采样方法，用于从非归一化玻尔兹曼分布中采样。核心创新在于利用一系列朗之万采样器，以高效模拟流过程：(i) 在中间时间生成插值分布的样本；(ii) 基于这些中间样本构建概率流ODE的速度场稳健估计器。理论上，我们为两个朗之万组件提供了收敛性保证，并建立了概率流ODE的非渐近收敛速率。大量数值实验表明，该方法在多种维度的挑战性多模态分布上表现高效，且在贝叶斯推断任务中具有显著有效性。
原文摘要 · Abstract (English)
We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a sequence of Langevin samplers to enable efficient simulation of the flow. Specifically, these Langevin samplers are employed (i) to generate samples from the interpolant distribution at intermediate times and (ii) to construct, starting from these intermediate times, a robust estimator of the velocity field governing the probability flow ODE. Theoretically, we provide convergence guarantees for both Langevin components, and establish a non-asymptotic convergence rate for the probability flow ODE. Extensive numerical experiments demonstrate the efficiency of the proposed method on challenging multimodal distributions across a range of dimensions, as well as its effectiveness in Bayesian inference tasks.
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