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）算法是计算统计学中从非归一化概率分布进行采样的重要工具，但在处理高维、多模态或复杂目标分布时可能表现脆弱。并行退火（PT）通过退火和并行计算提升了MCMC的采样效率，借助状态在插值分布间的交换，将样本从易于处理的参考分布传播至难以处理的目标分布。然而，在具有挑战性的问题中，相邻分布间通常存在极小重叠，这导致PT的有效性受到限制，需增加计算资源以弥补不足。我们提出一种框架，通过利用神经采样器（包括归一化流、扩散模型和受控扩散）加速PT，从而减少所需的重叠。该方法并行使用神经采样器，既规避了神经采样器的计算负担，又保持了经典PT的渐近一致性。我们在多种多模态采样问题上从理论和实证两方面证明，该方法能提升样本质量、相比经典PT降低计算成本，并实现高效的自由能/归一化常数估计。