In contrast to classic autoregressive generation, insertionbased models can predict in a order-free way multiple tokens at a time, which make their generation uniquely controllable: it can be constrained to strictly include an ordered list of tokens. We propose to exploit this feature in a new diverse paraphrasing framework: first, we extract important tokens or keywords in the source sentence; second, we augment them; third, we generate new samples around them by using insertion models. We show that the generated paraphrases are competitive with state of the art autoregressive paraphrasers, not only in diversity but also in quality. We further investigate their potential to create new pseudolabelled samples for data augmentation, using a meta-learning classification framework, and find equally competitive result. In addition to proving non-autoregressive (NAR) viability for paraphrasing, we contribute our open-source framework as a starting point for further research into controllable NAR generation.