  Score-based diffusion models provide a powerful way to model images using the
gradient of the data distribution. Leveraging the learned score function as a
prior, here we introduce a way to sample data from a conditional distribution
given the measurements, such that the model can be readily used for solving
inverse problems in imaging, especially for accelerated MRI. In short, we train
a continuous time-dependent score function with denoising score matching. Then,
at the inference stage, we iterate between numerical SDE solver and data
consistency projection step to achieve reconstruction. Our model requires
magnitude images only for training, and yet is able to reconstruct
complex-valued data, and even extends to parallel imaging. The proposed method
is agnostic to sub-sampling patterns, and can be used with any sampling
schemes. Also, due to its generative nature, our approach can quantify
uncertainty, which is not possible with standard regression settings. On top of
all the advantages, our method also has very strong performance, even beating
the models trained with full supervision. With extensive experiments, we verify
the superiority of our method in terms of quality and practicality.
