Generative models for network time series (also known as dynamic graphs) have tremendous potential in fields such as epidemiology, biology and economics, where complex graph-based dynamics are core objects of study. Designing flexible and scalable generative models is a very challenging task due to the high dimensionality of the data, as well as the need to represent temporal dependencies and marginal network structure. Here we introduce DAMNETS, a scalable deep generative model for network time series. DAMNETS outperforms competing methods on all of our measures of sample quality, over both real and synthetic data sets.