This paper introduces Sequential Monte Carlo (SMC) and diffusion-based sampling as effective methods for sampling from non-normalized probability densities. These methods rely on the idea of progressively propagating samples from a simple prior distribution to a complex target distribution. SMC propagates using Markov chains and resampling steps through successive annealing densities, while diffusion-based methods utilize learned dynamic propagation. In this paper, we present a principled framework that combines SMC and diffusion-based samplers by viewing both methods in continuous time and considering measures in path space. We then propose a novel Sequential Controlled Langevin Diffusion (SCLD) sampling method, which leverages the strengths of both methods to achieve performance improvements over conventional diffusion-based samplers on several benchmark problems at only 10% training cost.
