As you may have noticed, there is not much difference between our vanilla GAN and CGAN except that in CGANs, we are concatenating the additional input, which is the conditioning variable with the inputs of the generator and the discriminator. So, the loss function for both generator and discriminator is the same as the vanilla GAN with the exception that it is conditioned on .

Thus, the loss function of the discriminator is as follows:

The loss function of the generator is given as:

The CGAN learns by minimizing the loss function using gradient descent.