Variational diffusion models for blind MRI inverse problems

Motivation: Diffusion models have shown state-of-the-art performance in solving inverse problems. However, current solutions typically consider cases only when the forward operator is fully known, which limits their applicability to the wide variety of MRI inverse problems. Goal(s): Develop a general method for blind MRI inverse problems with unknown forward operator parameters. Approach: We extend the RED-diff framework, which has the key strength of not requiring training or fine–tuning for each specific task. We test our method for image reconstruction with off-resonance and motion correction. Results: Our blind RED-diff framework can successfully approximate the unknown forward model parameters and produce accurate reconstructions. Impact: We demonstrate the potential of current diffusion models to readily tackle a wide range of blind inverse problems in MRI without application-specific re-training or fine-tuning. Image reconstruction with motion and off-resonance correction are the first demonstration applications.