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Syntactically controlled paraphrase generation has become an emerging research direction in recent years. Most existing approaches require annotated paraphrase pairs for training and are thus costly to extend to new domains. Unsupervised approaches, on the other hand, do not need paraphrase pairs but suffer from relatively poor performance in terms of syntactic control and quality of generated paraphrases. In this paper, we demonstrate that leveraging Abstract Meaning Representations (AMR) can greatly improve the performance of unsupervised syntactically controlled paraphrase generation. Our proposed model, AMR-enhanced Paraphrase Generator (AMRPG), separately encodes the AMR graph and the constituency parse of the input sentence into two disentangled semantic and syntactic embeddings. A decoder is then learned to reconstruct the input sentence from the semantic and syntactic embeddings. Our experiments show that AMRPG generates more accurate syntactically controlled paraphrases, both quantitatively and qualitatively, compared to the existing unsupervised approaches. We also demonstrate that the paraphrases generated by AMRPG can be used for data augmentation to improve the robustness of NLP models.