https://arxiv.org/pdf/1906.02691.pdf
https://arxiv.org/pdf/1606.05908.pdf
$\huge f:\mathcal{Z}\times\mathcal{\Theta}\to\mathcal{X}$
$\huge f(z;\theta)\in\mathcal{X}$

typically,

or Bernoulli


So $\large Z\sim\mathcal{N}(0, I)$ is good enough.
Naïve integrate