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 entrapment.To 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 pattern.Experimental 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 https://anonymous.4open.science/r/ALIEN/.

翻译：水印技术是保护知识产权和减少滥用的技术手段。由于潜在扩散模型（LDMs）被视为生成任务的有力工具，现有方法主要集中于优化带水印的潜在变量，以平衡水印的鲁棒性和保真度。然而，依赖计算密集的启发式优化进行迭代信号优化，会导致高昂的训练开销和陷入局部最优解。为解决这些问题，我们提出了可控生成的分析式水印框架（ALIEN）。我们首次推导出时间相关的调制系数的解析解，该系数可引导水印残差的扩散，从而实现可控的水印嵌入模式。实验结果表明，ALIEN-Q 在 5 项质量指标上优于现有最优方法 33.1%，而 ALIEN-R 在 15 种不同条件下，针对生成变体和稳定性威胁的鲁棒性相比现有最优方法提升了 14.0%。代码可在 https://anonymous.4open.science/r/ALIEN/ 获取。