In the exciting generative AI era, the diffusion model has emerged as a very powerful and widely adopted content generation and editing tool for various data modalities, making the study of their potential security risks very necessary and critical. Very recently, some pioneering works have shown the vulnerability of the diffusion model against backdoor attacks, calling for in-depth analysis and investigation of the security challenges of this popular and fundamental AI technique. In this paper, for the first time, we systematically explore the detectability of the poisoned noise input for the backdoored diffusion models, an important performance metric yet little explored in the existing works. Starting from the perspective of a defender, we first analyze the properties of the trigger pattern in the existing diffusion backdoor attacks, discovering the important role of distribution discrepancy in Trojan detection. Based on this finding, we propose a low-cost trigger detection mechanism that can effectively identify the poisoned input noise. We then take a further step to study the same problem from the attack side, proposing a backdoor attack strategy that can learn the unnoticeable trigger to evade our proposed detection scheme. Empirical evaluations across various diffusion models and datasets demonstrate the effectiveness of the proposed trigger detection and detection-evading attack strategy. For trigger detection, our distribution discrepancy-based solution can achieve a 100\% detection rate for the Trojan triggers used in the existing works. For evading trigger detection, our proposed stealthy trigger design approach performs end-to-end learning to make the distribution of poisoned noise input approach that of benign noise, enabling nearly 100\% detection pass rate with very high attack and benign performance for the backdoored diffusion models.

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