The rapid proliferation of AI-generated images necessitates effective watermarking techniques to protect intellectual property and detect fraudulent content. While existing training-based watermarking methods show promise, they often struggle with generalizing across diverse prompts and tend to introduce visible artifacts. To this end, we propose a novel, provably generalizable image watermarking approach for Latent Diffusion Models, termed Self-Augmented Training (SAT-LDM). Our method aligns the training and testing phases through a free generation distribution, thereby enhancing the watermarking module's generalization capabilities. We theoretically consolidate SAT-LDM by proving that the free generation distribution contributes to its tight generalization bound, without the need for additional data collection. Extensive experiments show that SAT-LDM not only achieves robust watermarking but also significantly improves the quality of watermarked images across a wide range of prompts. Moreover, our experimental analyses confirm the strong generalization abilities of SAT-LDM. We hope that our method provides a practical and efficient solution for securing high-fidelity AI-generated content.