Amortized Posterior Sampling with Diffusion Prior Distillation
This addresses the problem of computationally expensive posterior sampling in inverse problems for researchers and practitioners in fields like imaging and climate science, offering an incremental improvement over existing methods.
The paper tackles efficient posterior sampling in inverse problems by proposing Amortized Posterior Sampling (APS), a variational inference approach that trains a conditional flow model to approximate the posterior distribution defined by a diffusion model, resulting in a sampler that generates diverse posterior samples with a single neural function evaluation. It demonstrates effectiveness on tasks like image restoration and climate data imputation, outperforming existing methods in computational efficiency while maintaining competitive reconstruction quality.
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.