This isn't possible as of now, at least not reliably. Yes, you can tailor a model to one specific generative model, but because we have no reliable outlier detection (to train the "AI made detector"), a generative model can always be trained with the detector model incorporated in the training process. The generative model (or a new model only designed to perturb output of the "original" generative model) would then learn to create outliers to the outlier detector, effectively fooling the detector. An outlier is everything that pretends to be "normal" but isn't.
In short: as of now we have no way to effectively and reliably defend against adversarial examples. This implies, that we have no way to effectively and reliably detect AI generated content.
Please correct me if I'm wrong, I might be mixing up some things.
I said "reliably", should have said "...and generally". You can, as I said, always tailor a detector model to a certain target model (generator). But the reliability of this defense builds upon the assumption, that the target model is static and doesn't change. This is has been a common error/mistake in AI research regarding defensive techniques against adversarial examples. And if you think about it, it's a very strong assumption, that doesn't make a lot of sense.
Again, learning the characteristics of one or several fixed models is trivial and gets us nowhere, because evasive techniques (e.g. finding 'adverserial examples against the detector' so to speak) can't be prevented as of know, to the best of my knowledge.
Edit: link to paper discussing problems of common defenses/attack scenario modelling https://proceedings.neurips.cc/paper/2020/hash/11f38f8ecd71867b42433548d1078e38-Abstract.html