Variational Diffusion Models for MRI Blind Inverse Problems

Diffusion models have demonstrated state-of-the-art results in solving inverse problems in various domains including medical imaging. However, existing works generally consider the cases where the forward operator is fully known. Therefore blind inverse problems with unknown forward operator parameters require modifications on existing methods. In this work, we present an extension of the recently developed regularization by denoising diffusion process (RED-diff) algorithm to the blind inverse problems. We test our method in fieldmap-corrected MR image reconstruction and show that the blind RED-diff framework can successfully approximate the unknown forward model parameters and produce fieldmap corrected reconstructions accurately.