This paper introduces image quality transfer. The aim is to learn the fine structural detail of medical images from high quality data sets acquired with long acquisition times or from bespoke devices and transfer that information to enhance lower quality data sets from standard acquisitions. We propose a framework for solving this problem using random forest regression to relate patches in the low-quality data set to voxel values in the high quality data set. Two examples in diffusion MRI demonstrate the idea. In both cases, we learn from the Human Connectome Project (HCP) data set, which uses an hour of acquisition time per subject, just for diffusion imaging, using custom built scanner hardware and rapid imaging techniques. The first example, super-resolution of diffusion tensor images (DTIs), enhances spatial resolution of standard data sets with information from the high-resolution HCP data. The second, parameter mapping, constructs neurite orientation density and dispersion imaging (NODDI) parameter maps, which usually require specialist data sets with two b-values, from standard single-shell high angular resolution diffusion imaging (HARDI) data sets with b = 1000smm−2. Experiments quantify the improvement against alternative image reconstructions in comparison to ground truth from the HCP data set in both examples and demonstrate efficacy on a standard data set.