提出一种基于序贯蒙特卡洛的扩散采样方法，高效估算目标分布的梯度与密度。
Diffusion Path Samplers via Sequential Monte Carlo
- 利用扩散路径和序贯蒙特卡洛，逐步从简单分布推导目标分布
- 在合成与真实数据集上实现低方差的分数估计，提升采样精度
- 适用于多种扩散路径，适合需要精确概率建模的研究者
我们为已知归一化常数外的分布开发了基于扩散的采样器。借助经典的扩散路径——从简单先验分布平滑过渡到目标分布，这一思路源自扩散模型。通过设计高效的序贯蒙特卡洛采样器，沿路径演化辅助变量，以条件分布为基础，为时变分布提供可证明的分数与密度估计。为控制分数估计的方差，进一步提出计算开销极小的控制变量调度策略。该框架被适配至奥恩斯坦-乌伦贝克（OU）逆时间过程、随机插值路径以及扩散退火朗之万动力学路径，并分析其权衡。最后，我们在多个合成与真实世界数据集上提供了理论保证与实证效果验证。
原文摘要 · Abstract (English)
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.
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