Changes over time in brain anatomy can provide important insight for treatment design or scientific analyses. We present a method that predicts how a brain MRI for an individual will change over time. We model changes using a diffeomorphic deformation field that we predict using function using convolutional neural networks. Given a predicted deformation field, a baseline scan can be warped to give a prediction of the brain scan at a future time. We demonstrate the method using the ADNI cohort, and analyze how performance is affected by model variants and the subject-specific information provided. We show that the model provides good predictions and that external clinical data can improve predictions.