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Many valid translations exist for a given sentence, yet machine translation (MT) is trained with a single reference translation, exacerbating data sparsity in low-resource settings. We introduce Simulated Multiple Reference Training (SMRT), a novel MT training method that approximates the full space of possible translations by sampling a paraphrase of the reference sentence from a paraphraser and training the MT model to predict the paraphraser’s distribution over possible tokens. We demonstrate the effectiveness of SMRT in low-resource settings when translating to English, with improvements of 1.2 to 7.0 BLEU. We also find SMRT is complementary to back-translation.