Large language models can produce highly fluent paraphrases while retaining much of the original meaning. While this capability has a variety of helpful applications, it may also be abused by bad actors, for example to plagiarize content or to conceal their identity. This motivates us to consider the problem of paraphrase inversion: given a paraphrased document, attempt to recover the original text. To explore the feasibility of this task, we fine-tune paraphrase inversion models, both with and without additional author-specific context to help guide the inversion process. We explore two approaches to author-specific inversion: one using in-context examples of the target author's writing, and another using learned style representations that capture distinctive features of the author's style. We show that, when starting from paraphrased machine-generated text, we can recover significant portions of the document using a learned inversion model. When starting from human-written text, the variety of source writing styles poses a greater challenge for invertability. However, even when the original tokens can't be recovered, we find the inverted text is stylistically similar to the original, which significantly improves the performance of plagiarism detectors and authorship identification systems that rely on stylistic markers.