Uncertainty-Aware 3D Residual Wavelet Diffusion for Ultra Low-Field MRI Super-Resolution

Ultra low-field MRI expands global access to neuroimaging but produces scans with low signal-to-noise ratio, reduced contrast, and thick slices. While regression-based super-resolution can recover anatomical detail for segmentation, it returns a single deterministic estimate that gives no indication of regions where the low-field input leaves anatomy underdetermined. Generative diffusion models offer an alternative by sampling the posterior distribution of plausible high-field images, quantifying this anatomical ambiguity. However, applying them to 3D whole-brain MRI is restricted by memory bottlenecks, slow sampling, and scanner domain shifts. We propose a 3D residual wavelet diffusion model that combines three ideas to overcome these hurdles. A lossless wavelet reparameterisation shrinks the spatial grid to fit a whole brain on a single GPU, residual shifting accelerates sampling by starting from the low-field input, and domain randomisation promotes scanner generalisation without paired training data. As the high-field reference is not a voxel-aligned ground truth, we evaluate downstream volumetric agreement. On a healthy cohort (n=19) imaged at 0.064T and 3T, our method matches a leading general-purpose regression approach in volumetric accuracy while additionally generating per-voxel uncertainty maps highlighting underdetermined regions. Furthermore, on a pilot dataset (n=11) of participants with cognitive impairment, disease-relevant atrophy is preserved rather than normalised towards a healthy prior. Our framework brings whole-brain posterior sampling to low-field super-resolution without sacrificing volumetric accuracy.