Methods, systems, and apparatus, including computer programs encoded on computer storage media, for predicting near-curb driving behavior. One of the methods includes obtaining agent trajectory data for an agent in an environment, the agent trajectory data comprising a current location and current values for a predetermined set of motion parameters of the agent; processing a model input generated from the agent trajectory data using a trained machine learning model to generate a model output comprising a prediction of whether the agent will exhibit near-curb driving behavior within a predetermined timeframe, wherein an agent exhibits near-curb driving behavior when the agent operates within a particular distance of an edge of a road in the environment; and using the prediction to generate a planned path for a vehicle in the environment.