We propose Generative Predecessor Models for Imitation Learning (GPRIL), a novel imitation learning algorithm that matches the state-action distribution to the distribution observed in expert demonstrations, using generative models to reason probabilistically about alternative histories of demonstrated states. We show that this approach allows an agent to learn robust policies using only a small number of expert demonstrations and self-supervised interactions with the environment. We derive this approach from first principles and compare it empirically to a state-of-the-art imitation learning method, showing that it outperforms or matches its performance on two simulated robot manipulation tasks and demonstrate significantly higher sample efficiency by applying the algorithm on a real robot.