Abstract: Text summarization aims to generate a short summary for an input text. In this work, we propose a Non-Autoregressive Unsupervised Summarization (NAUS) approach, which does not require parallel data for training. Our NAUS first performs edit-based search towards a heuristically defined score, and generates a summary as pseudo-groundtruth. Then, we train an encoder-only non-autoregressive Transformer based on the search result. We also proposed a dynamic programming approach for length-control decoding, which is important for the summarization task. Experiments on the Gigaword headline generation and DUC2004 datasets show that NAUS achieves state-of-the-art performance for unsupervised summarization, yet largely improving inference efficiency. Further, our algorithm is able to perform length-transfer summary generation.