Training Data Provenance Verification: Did Your Model Use Synthetic Data from My Generative Model for Training?

High-quality open-source text-to-image models have lowered the threshold for obtaining photorealistic images significantly, but also face potential risks of misuse. Specifically, suspects may use synthetic data generated by these generative models to train models for specific tasks without permission, when lacking real data resources especially. Protecting these generative models is crucial for the well-being of their owners. In this work, we propose the first method to this important yet unresolved issue, called Training data Provenance Verification (TrainProVe). The rationale behind TrainProVe is grounded in the principle of generalization error bound, which suggests that, for two models with the same task, if the distance between their training data distributions is smaller, their generalization ability will be closer. We validate the efficacy of TrainProVe across four text-to-image models (Stable Diffusion v1.4, latent consistency model, PixArt-$\alpha$, and Stable Cascade). The results show that TrainProVe achieves a verification accuracy of over 99\% in determining the provenance of suspicious model training data, surpassing all previous methods. Code will be publicly available soon.