We propose the Insertion-Deletion Transformer, a novel transformer-based neural architecture and training method for sequence generation. The model consists of two phases that are executed iteratively, 1) an insertion phase and 2) a deletion phase. The insertion phase parameterizes a distribution of insertions on the current output hypothesis, while the deletion phase parameterizes a distribution of deletions over the current output hypothesis. The training method is a principled and simple algorithm, where the deletion model obtains its signal directly on-policy from the insertion model output. We demonstrate the effectiveness of our Insertion-Deletion Transformer on synthetic translation tasks, obtaining significant BLEU score improvement over an insertion-only model.