[ivalm]

But this is not how generators work. They generally produce samples in the from

G: Q -> (X,Y)

where Q is some prior from which you are sampling. If they are not invertible then you straight up cannot get P(X,Y) out of the generator. Even if it is invertible getting P(X) requires integrating out the Y which might be infeasible (since the model is not integrable and is sufficiently fast changing that you need very, very many samples).