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The supervised training of high-capacity models on large datasets containing hundreds of thousands of document-summary pairs is critical to the recent success of deep learning techniques for abstractive summarization. Unfortunately, in most domains (other than news) such training data is not available and cannot be easily sourced. In this paper we enable the use of supervised learning for the setting where there are only documents available (e.g.,~product or business reviews) without ground truth summaries. We create a synthetic dataset from a corpus of user reviews by sampling a review, pretending it is a summary, and generating noisy versions thereof which we treat as pseudo-review input. We introduce several linguistically motivated noise generation functions and a summarization model which learns to denoise the input and generate the original review. At test time, the model accepts genuine reviews and generates a summary containing salient opinions, treating those that do not reach consensus as noise. Extensive automatic and human evaluation shows that our model brings substantial improvements over both abstractive and extractive baselines.