Mutations in viruses can result in zoonosis, immune escape, and changes in pathology. To control evolving pandemics, we wish to predict likely trajectories of virus evolution. Here we predict the probability of SARS-CoV-2 protein variants by using deep generative models to capture constraints on broader evolution of coronavirus sequences. We validate against lab measurements of mutant effects on replication and molecular function (e.g. receptor binding). We then apply our predictor to evaluate the potential of mutational escape from known antibodies, a strategy which can facilitate the development of antibody therapeutics and vaccines to mitigate immune evasion.