Progress in sentence simplification has been hindered by a lack of labeled\nparallel simplification data, particularly in languages other than English. We\nintroduce MUSS, a Multilingual Unsupervised Sentence Simplification system that\ndoes not require labeled simplification data. MUSS uses a novel approach to\nsentence simplification that trains strong models using sentence-level\nparaphrase data instead of proper simplification data. These models leverage\nunsupervised pretraining and controllable generation mechanisms to flexibly\nadjust attributes such as length and lexical complexity at inference time. We\nfurther present a method to mine such paraphrase data in any language from\nCommon Crawl using semantic sentence embeddings, thus removing the need for\nlabeled data. We evaluate our approach on English, French, and Spanish\nsimplification benchmarks and closely match or outperform the previous best\nsupervised results, despite not using any labeled simplification data. We push\nthe state of the art further by incorporating labeled simplification data.\n