Generative diffusion posterior sampling for informative likelihoods

Abstract: Sequential Monte Carlo (SMC) methods have recently shown successful results for conditional sampling of generative diffusion models. In this paper we propose a new diffusion posterior SMC sampler achieving improved statistical efficiencies, particularly under outlier conditions or highly informative likelihoods. The key idea is to construct an observation path that correlates with the diffusion model and to design the sampler to leverage this correlation for more efficient sampling. Empirical results conclude the efficiency.