Do you have some kind of dictionary where I can find this definition? Because I don’t really understand how that can be the deciding factor of „generative“, and the wiki page for „generative AI“ also seems to use the generic „AI that creates new stuff“ meaning.

By your definition, basically every classifier with 2 inputs would be generative. If I have a classifier for the MNIST dataset and my inputs are the pixels of the image, does that make the classifier generative because the inputs aren’t independent from each other?