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Most machine translation systems generate text autoregressively from left to right. We, instead, use a masked language modeling objective to train a model to predict any subset of the target words, conditioned on both the input text and a partially masked target translation. This approach allows for efficient iterative decoding, where we first predict all of the target words non-autoregressively, and then repeatedly mask out and regenerate the subset of words that the model is least confident about. By applying this strategy for a constant number of iterations, our model improves state-of-the-art performance levels for non-autoregressive and parallel decoding translation models by over 4 BLEU on average. It is also able to reach within about 1 BLEU point of a typical left-to-right transformer model, while decoding significantly faster.