We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or involve computationally expensive nested Markov chain Monte Carlo (MCMC) loops. In contrast, the proposed approach leverages stochastic averaging within a slow-fast system of stochastic differential equations (SDEs) to estimate intermediate scores along a diffusion path without training or inner-loop MCMC. Two algorithms are developed under this framework: MultALMC, which uses multiscale annealed Langevin dynamics, and MultCDiff, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process. Both overdamped and underdamped variants are considered, with theoretical guarantees of convergence to the desired diffusion path. The framework is extended to handle heavy-tailed target distributions using Student's t-based noise models and tailored fast-process dynamics. Empirical results across synthetic and real-world benchmarks, including multimodal and high-dimensional distributions, demonstrate that the proposed methods are competitive with existing samplers in terms of accuracy and efficiency, without the need for learned models.

翻译：本文提出了一种新颖的框架，通过利用多尺度动力学，从复杂的非归一化目标分布中高效采样。传统的基于分数的采样方法要么依赖于学习得到的分数函数近似，要么涉及计算成本高昂的嵌套马尔可夫链蒙特卡洛（MCMC）循环。相比之下，所提出的方法利用随机微分方程（SDEs）慢-快系统中的随机平均，沿扩散路径估计中间分数，无需训练或内层MCMC循环。在此框架下开发了两种算法：MultALMC，采用多尺度退火朗之万动力学；以及MultCDiff，基于多尺度受控扩散用于反向时间Ornstein-Uhlenbeck过程。同时考虑了过阻尼和欠阻尼变体，并提供了收敛到期望扩散路径的理论保证。该框架通过使用基于Student's t的噪声模型和定制的快速过程动力学，扩展至处理重尾目标分布。在合成和真实世界基准测试（包括多模态和高维分布）上的实证结果表明，所提出的方法在准确性和效率方面与现有采样器具有竞争力，且无需学习模型。