I'm having a very dense moment I think, and it's been far to long since the statistics courses.

They state the output of a neuron j is a log density P_j(y), where y is a latent variable.

But how does the output from the previous layer, x, come into play?

I guess I was expecting some kind of conditional probabilities, ie the output is P_j given x or something.

Again, perhaps trivial. Just struggling to figure out how it works in practice.

Clearly I wasn't in neural net mode. I take it then the learned parameters, the means, variances and mixing coefficients, are effectively functions of the output of the previous layer.