Recent work has shown that a multilingual neural machine translation (NMT) model can be used to judge how well a sentence paraphrases another sentence in the same language (Thompson and Post, 2020); however, attempting to generate paraphrases from such a model using standard beam search produces trivial copies or near copies. We introduce a simple paraphrase generation algorithm which discourages the production of n-grams that are present in the input. Our approach enables paraphrase generation in many languages from a single multilingual NMT model. Furthermore, the amount of lexical diversity between the input and output can be controlled at generation time. We conduct a human evaluation to compare our method to a paraphraser trained on the large English synthetic paraphrase database ParaBank 2 (Hu et al., 2019c) and find that our method produces paraphrases that better preserve meaning and are more gramatical, for the same level of lexical diversity. Additional smaller human assessments demonstrate our approach also works in two non-English languages.