why do we operate with graphical models in VAE, if there are no probabilites involved?

In the variational autoencoder, I often see graphical models e.g. $$P(X|Z)$$ for the decoder, but when I looked at code, I don't see any random variables, I see just deterministic network, with composite functions.

I am very confused by that, can someone explain where the magic happens? I am not interested in KL divergence and other stuff. I just don't understand how graphical model > $$P(X|Z)$$ == composite functions.