We propose a novel probabilistic generative model for action sequences. The model is termed the Action Point Process VAE (APP-VAE), a variational auto-encoder that can capture the distribution over the times and categories of action sequences. Modeling the variety of possible action sequences is a challenge, which we show can be addressed via the APP-VAE's use of latent representations and non-linear functions to parametrize distributions over which event is likely to occur next in a sequence and at what time. We empirically validate the efficacy of APP-VAE for modeling action sequences on the MultiTHUMOS and Breakfast datasets.