Extend SCLD to posterior sampling with pre-trained diffusion priors

Develop an extension of the Sequential Controlled Langevin Diffusion (SCLD) method for posterior sampling problems that leverage pre-trained diffusion priors by learning the likelihood score and incorporating Sequential Monte Carlo resampling steps during training, effectively combining an SMC-based posterior sampling framework with a log-variance–driven stochastic optimal control formulation for likelihood-score learning.

Background

The paper focuses on sampling from unnormalized densities using a new method, Sequential Controlled Langevin Diffusion (SCLD), which unifies diffusion-based samplers with Sequential Monte Carlo via path-space importance sampling and resampling.

In a related-works discussion, the authors describe posterior sampling settings where a pre-trained diffusion prior is available, along with methods that use SMC to correct biases in approximate likelihood scores and approaches that solve a stochastic optimal control problem via the log-variance divergence to learn the likelihood score.

They explicitly state that adapting SCLD to this posterior-sampling regime is left for future work and outline that it would correspond to combining an SMC-based posterior sampling method that leverages a diffusion prior with a log-variance–based SOC approach for learning the likelihood score.