Cascaded Posterior Sampling With Diffusion Priors for highly Accelerated MRI

Abstract

Diffusion models are powerful priors for inverse problems, including accelerated MRI. However, modeling the distribution of high-resolution images requires large networks with high computational cost. We propose a posterior sampling framework that uses cascaded diffusion models as multiscale priors. Conditioned on a coarse image, the distribution of fine-scale detail is local and well conditioned, and it can therefore be captured by a small network. Similarly, a small unconditional network is sufficient to represent low-resolution images, and it is used to recover the coarse image from the k-space center. This estimate then conditions the high-resolution prior, which is combined with all measurements to recover the final image. Both priors are trained on images alone, so they apply to any sampling pattern, and data consistency remains linear at every scale. In multi-coil brain MRI, the proposed method improves on the best single-scale diffusion baseline by 4-6 dB in PSNR at 15x acceleration, while each of its separately trained networks is about 10x smaller. The gain grows as the problem becomes more ill-posed, and ablations show that it arises from informative low-resolution conditioning.