Abstract: Paraphrase generation is a long-standing task in natural language processing (NLP). Supervised paraphrase generation models, which rely on human-annotated paraphrase pairs, are cost-inefficient and hard to scale up. On the other hand, automatically annotated paraphrase pairs (e.g., by machine back-translation), usually suffer from the lack of syntactic diversity -- the generated paraphrase sentences are very similar to the source sentences in terms of syntax. In this work, we present ParaAMR, a large-scale syntactically diverse paraphrase dataset created by abstract meaning representation back-translation. Our quantitative analysis, qualitative examples, and human evaluation demonstrate that the paraphrases of ParaAMR are syntactically more diverse compared to existing large-scale paraphrase datasets while preserving good semantic similarity. In addition, we show that ParaAMR can be used to improve on three NLP tasks: learning sentence embeddings, syntactically controlled paraphrase generation, and data augmentation for few-shot learning. Our results thus showcase the potential of ParaAMR for improving various NLP applications.