In recent years, advances in the fields of computational ethology and neuroscience have enabled detailed modeling of animal behavior and its neural underpinnings. However, these advances have yet to produce normative models of neuromotor control that generate the full diversity of animal behavior. Using recently developed methods in 3D pose estimation and deep reinforcement learning, we trained a latent variable model to control a virtual rodent body to imitate the natural behaviors of real rats in a physics simulator. Once trained, the model faithfully replicated diverse rat behaviors and generalized to unseen examples. We next sought out to quantify the extent to which the model’s latent representation of movement resembled that of neural activity in the dorsolateral striatum, a brain region implicated in the control of movement. We compared striatal neural activity recorded during unrestricted behavior in an open field to the model’s latent variables when imitating the same behaviors. The structure of neural activity across behavior was better predicted by the latent variable model than any other kinematic or dynamic feature of movement. This motivated us to analyze the ways in which the latent variables affected the model’s motor outputs. The model adaptively regulated variability in its motor outputs across behaviors, consistent with the minimum-intervention principle in optimal feedback control. We found that this was mediated by the regulation of latent variability, suggesting a computational mechanism through which the brain can regulate peripheral motor variability to support diverse behavior. These results demonstrate the utility of precise kinematic measurement, physical simulation, and artificial neural networks in modeling animal behavior, predicting the structure of neural activity across behavior, and generating novel hypotheses regarding the computational mechanisms underlying the neural control of movement.