In imitation learning, one aims to learn task-solving policies using access to near-optimal expert trajectories collected from the task environment. However, high-quality trajectories -- e.g., from human experts -- can be expensive to obtain in practical settings. On the contrary, it is often much easier to obtain large amounts of suboptimal trajectories which can nevertheless provide insight into the structure of the environment, showing what \emph{could} be done in the environment even if not what \emph{should} be done. Is it possible to formalize these conceptual benefits and devise algorithms to use offline datasets to yield \emph{provable} improvements to the sample-efficiency of imitation learning? In this work, we answer this question affirmatively and present training objectives which use an offline dataset to learn an approximate \emph{factored} dynamics model whose structure enables the extraction of a \emph{latent action space}. Our theoretical analysis shows that the learned latent action space can boost the sample-efficiency of downstream imitation learning, effectively reducing the need for large near-optimal expert datasets through the use of auxiliary non-expert data. We evaluate the practicality of our objective through experiments on a set of navigation and locomotion tasks. Our results verify the benefits suggested by our theory and show that our algorithms is able to recover near-optimal policies with fewer expert trajectories.