Recent advances in deep generative models have led to the development of methods capable of synthesizing high-quality, realistic images. These models pose threats to society due to their potential misuse. Prior research attempted to mitigate these threats by detecting generated images, but the varying traces left by different generative models make it challenging to create a universal detector capable of generalizing to new, unseen generative models. In this paper, we propose to inject a universal adversarial signature into an arbitrary pre-trained generative model, in order to make its generated contents more detectable and traceable. First, the imperceptible optimal signature for each image can be found by a signature injector through adversarial training. Subsequently, the signature can be incorporated into an arbitrary generator by fine-tuning it with the images processed by the signature injector. In this way, the detector corresponding to the signature can be reused for any fine-tuned generator for tracking the generator identity. The proposed method is validated on the FFHQ and ImageNet datasets with various state-of-the-art generative models, consistently showing a promising detection rate. Code will be made publicly available at \url{https://github.com/zengxianyu/genwm}.
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