Amid the burgeoning development of generative models like diffusion models, the task of differentiating synthesized audio from its natural counterpart grows more daunting. Deepfake detection offers a viable solution to combat this challenge. Yet, this defensive measure unintentionally fuels the continued refinement of generative models. Watermarking emerges as a proactive and sustainable tactic, preemptively regulating the creation and dissemination of synthesized content. Thus, this paper, as a pioneer, proposes the generative robust audio watermarking method (Groot), presenting a paradigm for proactively supervising the synthesized audio and its source diffusion models. In this paradigm, the processes of watermark generation and audio synthesis occur simultaneously, facilitated by parameter-fixed diffusion models equipped with a dedicated encoder. The watermark embedded within the audio can subsequently be retrieved by a lightweight decoder. The experimental results highlight Groot's outstanding performance, particularly in terms of robustness, surpassing that of the leading state-of-the-art methods. Beyond its impressive resilience against individual post-processing attacks, Groot exhibits exceptional robustness when facing compound attacks, maintaining an average watermark extraction accuracy of around 95%.