Diffusion models have rapidly become a vital part of deep generative architectures, given today's increasing demands. Obtaining large, high-performance diffusion models demands significant resources, highlighting their importance as intellectual property worth protecting. However, existing watermarking techniques for ownership verification are insufficient when applied to diffusion models. Very recent research in watermarking diffusion models either exposes watermarks during task generation, which harms the imperceptibility, or is developed for conditional diffusion models that require prompts to trigger the watermark. This paper introduces WDM, a novel watermarking solution for diffusion models without imprinting the watermark during task generation. It involves training a model to concurrently learn a Watermark Diffusion Process (WDP) for embedding watermarks alongside the standard diffusion process for task generation. We provide a detailed theoretical analysis of WDP training and sampling, relating it to a shifted Gaussian diffusion process via the same reverse noise. Extensive experiments are conducted to validate the effectiveness and robustness of our approach in various trigger and watermark data configurations.

翻译：扩散模型随着当今需求的不断增长，迅速成为深度生成架构的重要组成部分。获取大型高性能扩散模型需要大量资源，突显其作为值得保护的知识产权的重要性。然而，现有的所有权验证水印技术在应用于扩散模型时存在不足。近期关于扩散模型水印的研究要么在任务生成过程中暴露水印从而损害隐蔽性，要么是为需要提示触发水印的条件扩散模型而开发。本文提出WDM——一种新颖的扩散模型水印解决方案，无需在任务生成过程中嵌入水印。该方法通过训练模型在标准扩散过程（用于任务生成）的同时，学习水印扩散过程（WDP）以嵌入水印。我们提供了WDP训练与采样的详细理论分析，将其关联为通过相同反向噪声的平移高斯扩散过程。通过大量实验验证了该方法在不同触发条件和水印数据配置下的有效性和鲁棒性。