Distribution shifts, which often occur in the real world, degrade the accuracy of deep learning systems, and thus improving robustness is essential for practical applications. To improve robustness, we study an image enhancement method that generates recognition-friendly images without retraining the recognition model. We propose a novel image enhancement method, AugNet, which is based on differentiable data augmentation techniques and generates a blended image from many augmented images to improve the recognition accuracy under distribution shifts. In addition to standard data augmentations, AugNet can also incorporate deep neural network-based image transformation, which further improves the robustness. Because AugNet is composed of differentiable functions, AugNet can be directly trained with the classification loss of the recognition model. AugNet is evaluated on widely used image recognition datasets using various classification models, including Vision Transformer and MLP-Mixer. AugNet improves the robustness with almost no reduction in classification accuracy for clean images, which is a better result than the existing methods. Furthermore, we show that interpretation of distribution shifts using AugNet and retraining based on that interpretation can greatly improve robustness.