The images generated by generator has no labels, then how do Discriminator loss is generated on the basis of classification of generator generated images.
We already know that the images from the generator are fake and those from our training set are real. So, we assign them labels manually, real images as $0$ and fake ones as $1$, which gives us labelled data. Check the definition of loss function in any implementation of a GAN and you'll find that we assign the labels ourselves. For example, take a look here.
The Discriminator is just a binary classifier. You don't need labeled data as all the inputs are of same class.
So, Discriminator is considered as perfect classifier if it outputs
TRUE for input real image and
FALSE for generated image.
Discriminator loss is made up of two components:
Discriminator Real Loss: Prediction of real image as fake image Discriminator Fake Loss: Prediction of fake image as real image Discriminator Loss = Discriminator Real Loss + Discriminator Fake Loss