We propose DITTO, an offline imitation learning algorithm which uses world models and on-policy reinforcement learning to addresses the problem of covariate shift, without access to an oracle or any additional online interactions. We discuss how world models enable offline, on-policy imitation learning, and propose a simple intrinsic reward defined in the world model latent space that induces imitation learning by reinforcement learning. Theoretically, we show that our formulation induces a divergence bound between expert and learner, in turn bounding the difference in reward. We test our method on difficult Atari environments from pixels alone, and achieve state-of-the-art performance in the offline setting.