Data augmentation has proved extremely useful by increasing training data variance to alleviate overfitting and improve deep neural networks' generalization performance. In medical image analysis, a well-designed augmentation policy usually requires much expert knowledge and is difficult to generalize to multiple tasks due to the vast discrepancies among pixel intensities, image appearances, and object shapes in different medical tasks. To automate medical data augmentation, we propose a regularized adversarial training framework via two min-max objectives and three differentiable augmentation models covering affine transformation, deformation, and appearance changes. Our method is more automatic and efficient than previous automatic augmentation methods, which still rely on pre-defined operations with human-specified ranges and costly bi-level optimization. Extensive experiments demonstrated that our approach, with less training overhead, achieves superior performance over state-of-the-art auto-augmentation methods on both tasks of 2D skin cancer classification and 3D organs-at-risk segmentation.