We consider the problem of OOD generalization,where the goal is to train a model that performs well on test distributions that are different from the training distribution. Deep learning models are known to be fragile to such shifts and can suffer large accuracy drops even for slightly different test distributions (Hendrycks & Dietterich, 2019).We propose a new method –DAFT– based on the intuition that adversarially robust combination of a large number of rich features should provide OOD robustness. Our method carefully distills the model from a powerful teacher that learns several discriminative features using standard training while combining them using adversarial training. The standard adversarial training procedure is modified to produce teachers which can guide the student better. We evaluate DAFT on standard benchmarks in the DomainBed framework, and find that DAFT consistently out-performs well-tuned ERM and distillation baselines by up to 6%, with more pronounced gains for smaller networks