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 flow ODE. For both applications of the Langevin diffusions, we establish convergence guarantees. 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.

翻译：我们提出了一种基于线性随机插值导出的概率流常微分方程从未归一化玻尔兹曼密度进行采样的新方法。本方法的核心创新在于利用一系列Langevin采样器实现流的高效模拟。具体而言，这些Langevin采样器被用于：(i) 在中间时间点生成插值分布的样本；(ii) 从这些中间时间点出发，构建控制流常微分方程的速度场的鲁棒估计量。针对Langevin扩散在这两个应用场景中的表现，我们建立了收敛性保证。大量数值实验表明，所提方法在跨维度挑战性多峰分布上具有高效性，并在贝叶斯推断任务中展现出显著效果。