Diffusion models have emerged as state-of-the-art deep generative architectures with the increasing demands for generation tasks. Training large diffusion models for good performance requires high resource costs, making them valuable intellectual properties to protect. While most of the existing ownership solutions, including watermarking, mainly focus on discriminative models. This paper proposes WDM, a novel watermarking method for diffusion models, including watermark embedding, extraction, and verification. WDM embeds the watermark data through training or fine-tuning the diffusion model to learn a Watermark Diffusion Process (WDP), different from the standard diffusion process for the task data. The embedded watermark can be extracted by sampling using the shared reverse noise from the learned WDP without degrading performance on the original task. We also provide theoretical foundations and analysis of the proposed method by connecting the WDP to the diffusion process with a modified Gaussian kernel. Extensive experiments are conducted to demonstrate its effectiveness and robustness against various attacks.

翻译：扩散模型已成为生成任务中性能最优的深度生成架构，然而训练大规模扩散模型以实现良好性能需要高昂的资源成本，这使其成为具有重要保护价值的知识产权。现有所有权保护方案（包括水印技术）主要针对判别模型。本文提出WDM——一种面向扩散模型的新型水印方法，涵盖水印嵌入、提取与验证全流程。WDM通过训练或微调扩散模型学习水印扩散过程（WDP），该过程不同于任务数据的标准扩散过程，从而实现水印数据嵌入。通过从学习到的WDP中共享反向噪声进行采样，即可提取嵌入的水印，且不影响原始任务的性能。我们还将WDP与改进高斯核扩散过程建立理论关联，为本方法提供理论基础与分析。大量实验证明了该方法在多种攻击下的有效性与鲁棒性。