Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target distributions. Parallel Tempering (PT) enhances MCMC's sample efficiency through annealing and parallel computation, propagating samples from tractable reference distributions to intractable targets via state swapping across interpolating distributions. The effectiveness of PT is limited by the often minimal overlap between adjacent distributions in challenging problems, which requires increasing the computational resources to compensate. We introduce a framework that accelerates PT by leveraging neural samplers -- including normalising flows, diffusion models, and controlled diffusions -- to reduce the required overlap. Our approach utilises neural samplers in parallel, circumventing the computational burden of neural samplers while preserving the asymptotic consistency of classical PT. We demonstrate theoretically and empirically on a variety of multimodal sampling problems that our method improves sample quality, reduces the computational cost compared to classical PT, and enables efficient free energy/normalising constant estimation.

翻译：马尔可夫链蒙特卡洛（MCMC）算法是从非归一化概率分布中采样的计算统计学核心工具，但在处理高维、多模态或复杂目标分布时可能表现脆弱。并行回火（PT）通过退火与并行计算提升MCMC的采样效率，借助插值分布间的状态交换机制，将易处理的参考分布样本传递至难处理的目标分布。在复杂问题中，相邻分布间的重叠区域往往极小，这限制了PT的效能，需要增加计算资源以作补偿。本文提出一种利用神经采样器（包括归一化流、扩散模型及受控扩散过程）减少所需重叠区域的PT加速框架。该方法并行部署神经采样器，在保持经典PT渐近一致性的同时规避了神经采样器的计算负担。通过在多模态采样问题上的理论分析与实证研究，我们证明该方法能提升样本质量、降低相较于经典PT的计算成本，并实现高效的自由能/归一化常数估计。