We develop a diffusion-based sampler 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 distribution, widely used in diffusion models. Our approach is based on a practical implementation of diffusion-annealed Langevin Monte Carlo, which approximates the diffusion path with convergence guarantees. We tackle the score estimation problem by developing an efficient sequential Monte Carlo sampler that evolves auxiliary variables from conditional distributions along the path, which provides principled score estimates for time-varying distributions. We further develop novel control variate schedules that minimise the variance of these score estimates. Finally, we provide theoretical guarantees and empirically demonstrate the effectiveness of our method on several synthetic and real-world datasets.

翻译：本文提出了一种针对归一化常数未知的目标分布的扩散式采样器。为此，我们采用广泛应用于扩散模型的经典扩散路径，该路径可在（简单）基础分布与目标分布之间实现平滑插值。我们的方法基于扩散退火朗之万蒙特卡洛的实际实现，该实现能以收敛保证逼近扩散路径。针对得分估计问题，我们开发了一种高效的序贯蒙特卡洛采样器，该采样器沿路径从条件分布演化辅助变量，从而为时变分布提供理论严谨的得分估计。我们进一步设计了新型控制变量调度方案，以最小化这些得分估计的方差。最后，我们提供了理论保证，并在多个合成与真实数据集上实证验证了本方法的有效性。