Homogenising the availability of manually generated information in large databases has been a key challenge of medical imaging for many years. Due to the time consuming nature of manually segmenting, parcellating and localising landmarks in medical images, these sources of information tend to be scarce and limited to small, and sometimes morphologically similar, subsets of data. In this work we explore a new framework where these sources of information can be propagated to morphologically dissimilar images by diffusing and mapping the information through intermediate steps. The spatially variant data embedding uses the local morphology and intensity similarity between images to diffuse the information only between locally similar images. This framework can thus be used to propagate any information from any group of subject to every other subject in a database with great accuracy. Comparison to state-of-the-art propagation methods showed highly statistically significant (p < 10(-4)) improvements in accuracy when propagating both structural parcelations and brain segmentations geodesically.