I have been reading and looking at implementations of the SRGAN, from "Photo-realistic Single Image Super Resolution with Generative Adversarial Networks" paper. One thing that I noticed is that the SRGAN formulation does not consider a noise Z on it's input, unlike normal GANs/cGANs. In Super Resolution we want the model to learn to generate samples from a certain distribution (human faces) that are conditioned to a certain Low Resolution(LR) Image (must be that specific person), therefore isn't it a cGAN? But why we don't see any random noise as input on SRGAN? Would the G (LR image) be the G(z | y) of the cGAN?
It is not clear to me that SRGAN uses the idea of cGANs, since we don't pass any random noise as input, only the LR image (deterministic, at least in the paper case).
The SRGAN formulation follows: