# Use of random noise in Generative adversarial networks

I was reading Image to Image Translation with Conditional Adversarial Networks. On its third page, it states that

Without z, the net could still learn a mapping from x to y, but would produce deterministic outputs, and therefore fail to match any distribution other than a delta function.

Here z is the random noise given to the generator as input. x refers to the labels fed as input for Conditional Adversarial Networks.

Can somebody please explain the above paragraph.

For a simpler version of this, recall that MSE linear regression can be interpreted as a Maximum Likelihood procedure for $\beta$ where $y = X\beta + \epsilon$, $\epsilon$ being normally distributed noise.