Abstract: Diffusion models have recently delivered state-of-the-art performance for MRI reconstruction with improved robustness. However, these models fail when there is a large distribution shift, and their long inference times impede their clinical utility. Recently, regularization by denoising diffusion process (RED-diff) was introduced for solving general inverse problems. RED-diff uses a variational sampler based on a measurement consistency loss and a score matching regularization. In this paper, we extend RED-diff to MRI reconstruction. RED-diff formulates MRI reconstruction as stochastic optimization, and outperforms diffusion baselines in PSNR/SSIM with $3 \times$ faster inference while using the same amount of memory. The code is publicly available at https://github.com/NVlabs/SMRD.