In order to diagnose, monitor, and eventually cure a disease, quantitative measures of abnormality are required. If reference growth curves are available for child developmental disorders, building normative scenarii of alterations for neuro-degenerative diseases, which slowly develop over years, remains an open problem. Two main difficulties explains this. First, relevant and objective markers of progression most often come from medical imaging, and are therefore very high-dimensional and structured measurements. As a consequence, the subtle temporal individual changes are easily masked by the large innate and normal variability of the population. Second, a disease like Alzheimer's may start developing at any age and at any pace. Therefore no common time-line is explicitly available to compare individual health records. Based on the large deformation diffeomorphic metric mapping framework, this paper introduces unified modeling approach that jointly learns a mean progression pattern along with temporal and geometrical variance estimates from unaligned temporal progressions of imaging measurements. Normal distributions of shape trajectories are defined as generative and hierarchical statistical models, which are learned by an original calibration algorithm. Based on the estimated normative scenarii, vizualisation, correlation, classification and simulation tasks are naturally defined and carried out. Proposed algorithms are validated on a simulated data set, illustrated on video sequences of emotive faces, and applied on a medical data set of Alzheimer's patients. Atrophy-protective genetic, biological and environmental cofactors are identified.