Without positional information, attention-based transformer neural networks are permutation-invariant. Absolute or relative positional embeddings are the most popular ways to feed transformer models positional information. Absolute positional embeddings are simple to implement, but suffer from generalization issues when evaluating on sequences of different length than those seen at training time. Relative positions are more robust to length change, but are more complex to implement and yield inferior model throughput. In this paper, we propose an augmentation-based approach (CAPE) for absolute positional embeddings, which keeps the advantages of both absolute (simplicity and speed) and relative position embeddings (better generalization). In addition, our empirical evaluation on state-of-the-art models in machine translation, image and speech recognition demonstrates that CAPE leads to better generalization performance as well as increased stability with respect to training hyper-parameters.