[zozbot234]

You can derive the latter information (the joint distribution), given the former and a prior over "all pixels"-like data. So, the defining feature of "generative" models is that they feature a prior over their input data?

[Nimitz14]

Generative models model the data, whether that is p(x) or p(x,y) or (x,y,z) etc.

[currymj]

Yes, though maybe not explicitly written down.