Methods, systems, and apparatus, including computer programs encoded on computer storage media, for predicting the future movement of agents in an environment. In particular, the future movement is predicted through occupancy flow fields that specify, for each future time point in a sequence of future time points and for each agent type in a set of one or more agent types: an occupancy prediction for the future time step that specifies, for each grid cell, an occupancy likelihood that any agent of the agent type will occupy the grid cell at the future time point, and a motion flow prediction that specifies, for each grid cell, a motion vector that represents predicted motion of agents of the agent type within the grid cell at the future time point.