Learning from expert demonstrations is an attractive framework for sequential decision-making in safety-critical domains such as autonomous driving, where trial and error learning has no safety guarantees during training. However, naïve use of imitation learning can fail by extrapolating incorrectly to unfamiliar situations, resulting in arbitrary model outputs and dangerous outcomes. This is especially true for high capacity parametric models such as deep neural networks, for process- ing high-dimensional observations from cameras or LIDAR. Instead, we model expert behaviour with a model able to capture uncertainty about previously unseen scenarios, as well as inherent stochasticity in expert demonstrations. We propose a framework for planning under epistemic uncertainty and also provide a practical realisation, called robust imitative planning (RIP), using an ensemble of deep neural density estimators. We demonstrate online robustness to out-of-training- distribution scenarios on the CARLA autonomous driving simulator, improving over other probabilistic imitation learning models and reducing the total number of hazardous events while improving runtime to real-time using a trajectory library.