We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised by diffusion models. We tackle the score estimation problem by developing an efficient sequential Monte Carlo sampler that evolves auxiliary variables from conditional distributions along the path, providing principled score and density estimates for time-varying distributions. To control the variance of score estimates, we further propose practical control variate schedules that incur minimal overhead. We adapt this general framework to paths induced by the Ornstein-Uhlenbeck (OU) time-reversal process, stochastic interpolants, and diffusion annealed Langevin dynamics, outlining their trade-offs. Finally, we provide theoretical guarantees and empirically demonstrate the effectiveness of our method on several synthetic and real-world datasets.

翻译：我们开发了基于扩散的采样器，用于仅已知归一化常数的目标分布。为此，我们依赖扩散模型中广为人知的扩散路径，该路径在简单基分布与目标之间平滑插值。通过开发高效的序贯蒙特卡洛采样器，沿路径从条件分布中演化辅助变量，我们解决了分数估计问题，为随时间变化的分布提供了有原则的分数和密度估计。为控制分数估计的方差，我们进一步提出了实用的控制变量调度方案，且仅带来极小的计算开销。我们将此通用框架应用于奥恩斯坦-乌伦贝克时间逆过程、随机插值以及扩散退火朗之万动力学所诱导的路径，并概述了它们各自的权衡。最后，我们提供了理论保证，并在多个合成及真实世界数据集上实验证明了该方法的有效性。