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Watermarking is a technical alternative to safeguarding intellectual property and reducing misuse. Existing methods focus on optimizing watermarked latent variables to balance watermark robustness and fidelity, as Latent diffusion models (LDMs) are considered a powerful tool for generative tasks. However, reliance on computationally intensive heuristic optimization for iterative signal refinement results in high training overhead and local optima this http URL address these issues, we propose an \underline{A}na\underline{l}ytical Watermark\underline{i}ng Framework for Controllabl\underline{e} Generatio\underline{n} (ALIEN). We develop the first analytical derivation of the time-dependent modulation coefficient that guides the diffusion of watermark residuals to achieve controllable watermark embedding this http URL results show that ALIEN-Q outperforms the state-of-the-art by 33.1\% across 5 quality metrics, and ALIEN-R demonstrates 14.0\% improved robustness against generative variant and stability threats compared to the state-of-the-art across 15 distinct conditions. Code can be available at this https URL.