Amortized Posterior Sampling with Diffusion Prior Distillation

Abbas Mammadov, Hyungjin Chung, Jong Chul Ye

Keywords: Inverse Problems, Diffusion Models, Variational Inference

Abstract:

We propose Amortized Posterior Sampling (APS), a novel variational inference approach for efficient posterior sampling in inverse problems.
Our method trains a conditional flow model to minimize the divergence between the variational distribution and the posterior distribution implicitly defined by the diffusion model.
This results in a powerful, amortized sampler capable of generating diverse posterior samples with a single neural function evaluation, generalizing across various measurements.
Unlike existing methods, our approach is unsupervised, requires no paired training data, and is applicable to both Euclidean and non-Euclidean domains.
We demonstrate its effectiveness on a range of tasks, including image restoration, manifold signal reconstruction, and climate data imputation.
APS significantly outperforms existing approaches in computational efficiency while maintaining competitive reconstruction quality, enabling real-time, high-quality solutions to inverse problems across diverse domains.

Submission Number: 59