Most approaches to machine learning from electronic health data can only predict a single endpoint. Here, we present an alternative that uses unsupervised deep learning to simulate detailed patient trajectories. We use data comprising 18-month trajectories of 44 clinical variables from 1908 patients with Mild Cognitive Impairment or Alzheimer's Disease to train a model for personalized forecasting of disease progression. We simulate synthetic patient data including the evolution of each sub-component of cognitive exams, laboratory tests, and their associations with baseline clinical characteristics, generating both predictions and their confidence intervals. Our unsupervised model predicts changes in total ADAS-Cog scores with the same accuracy as specifically trained supervised models and identifies sub-components associated with word recall as predictive of progression. The ability to simultaneously simulate dozens of patient characteristics is a crucial step towards personalized medicine for Alzheimer's Disease.