  We propose to study and promote the robustness of a model as per its
performance through the interpolation of training data distributions.
Specifically, (1) we augment the data by finding the worst-case Wasserstein
barycenter on the geodesic connecting subpopulation distributions of different
categories. (2) We regularize the model for smoother performance on the
continuous geodesic path connecting subpopulation distributions. (3)
Additionally, we provide a theoretical guarantee of robustness improvement and
investigate how the geodesic location and the sample size contribute,
respectively. Experimental validations of the proposed strategy on
\textit{four} datasets, including CIFAR-100 and ImageNet, establish the
efficacy of our method, e.g., our method improves the baselines' certifiable
robustness on CIFAR10 up to $7.7\%$, with $16.8\%$ on empirical robustness on
CIFAR-100. Our work provides a new perspective of model robustness through the
lens of Wasserstein geodesic-based interpolation with a practical off-the-shelf
strategy that can be combined with existing robust training methods.
