An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where the transport is performed through successive annealed densities via prescribed Markov chains and resampling steps, and (2) recently developed diffusion-based sampling methods, where a learned dynamical transport is used. Despite the common goal, both approaches have different, often complementary, advantages and drawbacks. The resampling steps in SMC allow focusing on promising regions of the space, often leading to robust performance. While the algorithm enjoys asymptotic guarantees, the lack of flexible, learnable transitions can lead to slow convergence. On the other hand, diffusion-based samplers are learned and can potentially better adapt themselves to the target at hand, yet often suffer from training instabilities. In this work, we present a principled framework for combining SMC with diffusion-based samplers by viewing both methods in continuous time and considering measures on path space. This culminates in the new Sequential Controlled Langevin Diffusion (SCLD) sampling method, which is able to utilize the benefits of both methods and reaches improved performance on multiple benchmark problems, in many cases using only 10% of the training budget of previous diffusion-based samplers.

翻译：从非归一化密度中采样的有效方法基于将样本从简单先验逐步传输到复杂目标分布的思想。两种流行方法是：(1) 序列蒙特卡洛(SMC)，通过预设马尔可夫链和重采样步骤在逐次退火密度间实现传输；(2) 近期发展的基于扩散的采样方法，采用学习得到的动态传输机制。尽管目标相同，两种方法却具有不同且往往互补的优势与局限。SMC中的重采样步骤能够聚焦于空间中的优势区域，通常带来稳健性能。虽然该算法具有渐近保证，但缺乏灵活可学习的转移机制可能导致收敛缓慢。另一方面，基于扩散的采样器通过学习获得，可能更好地适应特定目标分布，但常受训练不稳定性困扰。本研究提出将SMC与基于扩散的采样器相结合的原则性框架，通过在连续时间视角下考察两种方法并考虑路径空间上的测度。由此发展出新型序列控制朗之万扩散采样方法，该方法能综合利用两种技术的优势，在多个基准问题上实现性能提升，且在许多情况下仅需先前基于扩散的采样器10%的训练计算量。