Diffusion Path Samplers via Sequential Monte Carlo

We develop a diffusion-based sampler for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a (simple) base distribution and the target distribution, widely used in diffusion models. Our approach is based on a practical implementation of diffusion-annealed Langevin Monte Carlo, which approximates the diffusion path with convergence guarantees. We tackle the score estimation problem by developing an efficient sequential Monte Carlo sampler that evolves auxiliary variables from conditional distributions along the path, which provides principled score estimates for time-varying distributions. We further develop novel control variate schedules that minimise the variance of these score estimates. Finally, we provide theoretical guarantees and empirically demonstrate the effectiveness of our method on several synthetic and real-world datasets.

💡 Research Summary

This paper addresses the fundamental problem of sampling from a probability distribution π that is known only up to a normalising constant, a task that underlies Bayesian inference, machine learning, statistical physics, finance, and computational biology. Traditional approaches often introduce an auxiliary path of intermediate distributions that bridges a simple base density ν and the target π, allowing the sampler to gradually adapt to the target’s complexity. While geometric paths have been popular, they can create spurious modes and degrade functional inequalities, leading to poor performance. The authors instead focus on diffusion paths, which have recently become central in generative modeling. A diffusion path µ_t, t∈