Abstract: This paper presents two strong methods, CTC and Imputer, for non-autoregressive machine translation that model latent alignments with dynamic programming. We revisit CTC for machine translation and demonstrate that a simple CTC model can achieve state-of-the-art for single-step non-autoregressive machine translation, contrary to what prior work indicates. In addition, we adapt the Imputer model for non-autoregressive machine translation and demonstrate that Imputer with just 4 generation steps can match the performance of an autoregressive Transformer baseline. Our latent alignment models are simpler than many existing non-autoregressive translation baselines; for example, we do not require target length prediction or re-scoring with an autoregressive model. On the competitive WMT'14 En$\rightarrow$De task, our CTC model achieves 25.7 BLEU with a single generation step, while Imputer achieves 27.5 BLEU with 2 generation steps, and 28.0 BLEU with 4 generation steps. This compares favourably to the autoregressive Transformer baseline at 27.8 BLEU.