Foundational generative models should be traceable to protect their owners and facilitate safety regulation. To achieve this, traditional approaches embed identifiers based on supervisory trigger-response signals, which are commonly known as backdoor watermarks. They are prone to failure when the model is fine-tuned with nontrigger data. Our experiments show that this vulnerability is due to energetic changes in only a few 'busy' layers during fine-tuning. This yields a novel arbitrary-in-arbitrary-out (AIAO) strategy that makes watermarks resilient to fine-tuning-based removal. The trigger-response pairs of AIAO samples across various neural network depths can be used to construct watermarked subpaths, employing Monte Carlo sampling to achieve stable verification results. In addition, unlike the existing methods of designing a backdoor for the input/output space of diffusion models, in our method, we propose to embed the backdoor into the feature space of sampled subpaths, where a mask-controlled trigger function is proposed to preserve the generation performance and ensure the invisibility of the embedded backdoor. Our empirical studies on the MS-COCO, AFHQ, LSUN, CUB-200, and DreamBooth datasets confirm the robustness of AIAO; while the verification rates of other trigger-based methods fall from ∼90% to ∼70% after fine-tuning, those of our method remain consistently above 90%.

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