The task of predicting human motion is complicated by the natural heterogeneity and compositionality of actions, necessitating robustness to distributional shifts as far as out-of-distribution (OoD). Here, we formulate a new OoD benchmark based on the Human3.6M and Carnegie Mellon University (CMU) motion capture datasets, and introduce a hybrid framework for hardening discriminative architectures to OoD failure by augmenting them with a generative model. When applied to current state-of-the-art discriminative models, we show that the proposed approach improves OoD robustness without sacrificing in-distribution performance, and can theoretically facilitate model interpretability. We suggest human motion predictors ought to be constructed with OoD challenges in mind, and provide an extensible general framework for hardening diverse discriminative architectures to extreme distributional shift. The code is available at: https://github.com/bouracha/OoDMotion.