Physics-Informed Cold Diffusion Framework with Time-Conditioned U-Net for Multi-Coil Brain MRI Reconstruction

Magnetic Resonance Imaging (MRI) reconstruction from undersampled multi-coil k-space data remains acentral challenge for accelerating clinical scans. This paper proposes a cold diffusion based reconstructionframework that integrates a deterministic k-space forward operator with a time-conditioned U-Netdenoiser. Unlike conventional diffusion models that rely on stochastic Gaussian noise, the proposed approachexplicitly models the physical undersampling process, yielding interpretable and data-consistentreconstructions. The model was trained and evaluated on the fastMRI multi-coil brain dataset using 2Dslices center-cropped to 320×320 and normalized in complex form (real + imaginary channels). Ablationstudies compare the proposed method against a supervised U-Net baseline and a Gaussian DDPM trainedunder identical conditions. Quantitatively, the cold diffusion model with 500 diffusion steps achieved 37.8dB PSNR, 0.42 SSIM, and 0.46 HFEN, outperforming both the DDPM (32.8 dB, 0.33 SSIM, 0.60 HFEN)and supervised U-Net (28.9 dB, 0.29 SSIM, 0.71 HFEN) while reducing inference time by 70% relativeto conventional diffusion sampling. Qualitative results indicate improved anatomical sharpness, stableconvergence and consistent reconstruction across slices, suggesting that the physics-informed diffusionframework is a reliable and interpretable approach for accelerated MRI reconstruction.