CM-RED

A diffusion prior can reconstruct an eightfold-undersampled brain scan with convincing anatomical detail, and spend a thousand passes through the network doing it. The cost is structural: a diffusion model learns an average denoising direction at each noise level, so a clean image means walking the trajectory one small step at a time. Consistency models remove the walk — one function evaluation maps any point on the trajectory to its clean endpoint.

CM-RED uses that property inside an iterative reconstruction rather than as a sampler, placing a pretrained consistency model as the proximal operator in a regularization-by-denoising (RED) scheme. It builds on accelerated proximal gradient RED and adds two ingredients that make few-step operation work: controlled Gaussian noise injected before each prior update, and momentum after each data-fidelity update. Accelerated multi-coil MRI is reconstructed in four network function evaluations. It comes from the group of Mehmet Akçakaya in the Center for Magnetic Resonance Research at the University of Minnesota, posted to arXiv in August 2026 as an extended version of a preliminary IEEE ISBI 2026 conference paper.

What makes the prior a model of MR anatomy rather than a general inverse-problem solver is that it is unconditional and never sees the acquisition: it is trained only on complex-valued coil-combined knee and brain images from fastMRI, with no knowledge of the sampling mask, acceleration rate or encoding operator. One frozen checkpoint per anatomy serves fourfold and eightfold undersampling, equidistant and Gaussian-1D patterns, and six contrast weightings it never saw. That separation places CM-RED alongside PhaseGen as a complex-valued generative prior over raw MR data, and apart from unrolled networks trained end to end for one protocol.

#Key Features

• Four-step reconstruction: Each of four outer iterations applies one prior update, then a data-fidelity update solved with 10 conjugate-gradient steps, from a CG-SENSE initialization. Diffusion-based solvers in the same comparison use 100 to 1,000 evaluations.
• Controlled noise injection: A consistency model approaches an identity map as the denoising level goes to zero, so it barely corrects a nearly clean iterate. Perturbing the iterate before each prior call forces a larger corrective update, which is what allows four-step convergence to work.
• Explicit multi-coil data fidelity: The measurement update solves a quadratic penalized least-squares problem against the SENSE encoding operator rather than a pseudo-inverse back-projection, which amplifies noise at high acceleration.
• Hyperparameters shared across anatomy and contrast: One setting covers every anatomy, contrast and sampling pattern, differing only between acceleration rates; perturbing all of them by ±10% shifts PSNR within roughly ±0.2 dB.

#Technical Details

The prior is a complex-valued UNet from the guided-diffusion family at 320×320, with 256 base channels, two residual blocks per resolution, multi-resolution attention and no class conditioning; real and imaginary components enter as separate channels. The knee prior comes from the authors' earlier conference work; the brain prior was trained from scratch on A100 GPUs in two stages — an EDM diffusion model for 700K iterations, then consistency distillation for 1.05M — using 973 fastMRI knee subjects and 4,267 brain subjects. Evaluation covered 10 held-out subjects, 1,095 slices spanning coronal PD and PD-FS knee and axial T1-pre, T1-post, T2 and FLAIR brain scans, undersampled at R = 4 and R = 8. Under equidistant undersampling at R = 4, CM-RED reaches 36.58 dB PSNR and 0.927 SSIM on coronal PD and 40.61 dB / 0.969 on axial T1-pre, against 34.82 dB / 0.886 for DPS at 1,000 evaluations and 34.86 dB / 0.901 for DDS at 100. It leads on both metrics in nearly every configuration tested.

#Applications

The target use is undersampled Cartesian MRI, where shortening a scan is clinically valuable and reconstruction latency decides whether a generative prior is deployable. Because the prior is decoupled from the acquisition, a site can change acceleration rate, undersampling pattern or pulse sequence without retraining. The released code and checkpoints reconstruct fastMRI knee and brain data directly, and the scheme extends to other anatomies for groups able to train a prior on their own fully sampled images.

#Impact

CM-RED shows that consistency models can serve as few-step generative priors for a physics-based medical imaging inverse problem, closing much of the gap between diffusion-quality reconstructions and the compute budget of a clinical workflow. Its limitations are stated plainly by the authors: the priors require fully sampled training data, often unavailable in clinical archives; the reconstruction depends on several hand-tuned hyperparameters; distilling the underlying diffusion model stays expensive even though inference is cheap; and evaluation is confined to Cartesian retrospective undersampling, with no non-Cartesian trajectories or patient cohorts. The extended arXiv version has not been peer reviewed, though the preliminary version was accepted at ISBI 2026. The repository publishes the source code and links both checkpoints but carries no license file, and fastMRI is available only under NYU's data use agreement.