Our goal is to train control policies that generalize well to unseen environments. Inspired by the Distributionally Robust Optimization (DRO) framework, we propose DRAGEN - Distributionally Robust policy learning via Adversarial Generation of ENvironments - for iteratively improving robustness of policies to realistic distribution shifts by generating adversarial environments. The key idea is to learn a generative model for environments whose latent variables capture cost-predictive and realistic variations in environments. We perform DRO with respect to a Wasserstein ball around the empirical distribution of environments by generating realistic adversarial environments via gradient ascent on the latent space. We demonstrate strong Out-of-Distribution (OoD) generalization in simulation for (i) swinging up a pendulum with onboard vision and (ii) grasping realistic 2D/3D objects. Grasping experiments on hardware demonstrate better sim2real performance compared to domain randomization.