Follow-up imaging studies require the evaluation of the anatomical changes over time for specific clinical groups. The longitudinal changes for a specific subject can be evaluated through the non-rigid registration of successive anatomical images. However, to perform a longitudinal group-wise analysis, the subject-specific longitudinal trajectories of anatomical points need to be transported in a common reference frame. In this work, we propose the Schild's Ladder framework as an effective method to transport longitudinal deformations in time series of images in a common space using diffeomorphic registration. We illustrate the computational advantages and demonstrate the numerical accuracy of this very simple method by comparing with standard methods of transport on simulated images with progressing brain atrophy. Finally, its application to the clinical problem of the measurement of the longitudinal progression in the Alzheimer's disease suggests that an important gain in sensitivity could be expected on group-wise comparisons.