The advancements in audio generative models have opened up new challenges in their responsible disclosure and the detection of their misuse. In response, we introduce a method to watermark latent generative models by a specific watermarking of their training data. The resulting watermarked models produce latent representations whose decoded outputs are detected with high confidence, regardless of the decoding method used. This approach enables the detection of the generated content without the need for a post-hoc watermarking step. It provides a more secure solution for open-sourced models and facilitates the identification of derivative works that fine-tune or use these models without adhering to their license terms. Our results indicate for instance that generated outputs are detected with an accuracy of more than 75% at a false positive rate of $10^{-3}$, even after fine-tuning the latent generative model.