We introduce a dynamics-level approach to watermarking generative models. Rather than embedding signals into model weights or outputs, we embed the watermark directly into the learned continuous dynamics -- the velocity field of a flow matching model. We formulate this as random coding over a continuous channel: a key-dependent perturbation is added during training, and the message is recovered at detection time from black-box queries. The perturbation is designed to leave the generated distribution unchanged. Experiments on MNIST and CIFAR-10 across different architectures confirm reliable message recovery, preserved generation quality, and chance-level decoding accuracy without the secret key.

翻译：我们提出一种面向生成模型的动态层级水印方法。与传统的将信号嵌入模型权重或输出不同，本方法将水印直接植入模型学习到的连续动态过程——即流匹配模型的速度场中。我们将该过程建模为连续信道上的随机编码：在训练阶段引入密钥相关的扰动，检测阶段通过黑盒查询恢复隐藏信息。该扰动设计确保生成数据分布不发生改变。基于不同架构的MNIST与CIFAR-10数据集实验证实：该方法可实现可靠的信息恢复、保持生成质量，且在无密钥条件下解码准确率仅达随机水平。