The rapid improvement of LLMs has made distinguishing AI-generated text from human writing a pressing problem. This challenge is further amplified by paraphrasing tools designed to make machine-generated text appear more "human".

We study how access to human writing samples can be used to strategically paraphrase machine-generated responses toward the human distribution. Under a multi-sample setting with human and machine responses to the same prompts, we show that repeated paraphrasing moves the machine distribution toward the empirical human distribution under simple mixing and stability conditions.

Our results derive an explicit convergence rate, extend the analysis to a finite-sample setting, and characterize how the required number of human samples and paraphrasing rounds scale with the desired error.