How do GAN's generator actually work?

Question

I have implemented DCGAN's myself and have been studying GAN's for over a month now. Now I am implementing the pggans but I encountered a sentence

When we measure the distance between the training distribution and the generated distribution, the gradients can point to more or less random directions if the distributions do not have substantial overlap (https://arxiv.org/pdf/1710.10196.pdf)

but we do never compare the distribution between training and generated distributions in gans a far I know when we train the gan

fixed_noise = to.randn(num_test_samples, 100).view(-1,100, 1, 1)
for epoch in range(opt.number_epochs):
D_losses = []
G_losses = []
for i,(images, labels) in enumerate(dataloader):
    minibatch = images.size()[0]
    real_images = Variable(images.cuda()) 
    real_labels = Variable(to.ones(minibatch).cuda())
    fake_labels = Variable(to.zeros(minibatch).cuda())
    ##Train discriminator
    #First with real data 
    D_real_Decision = discriminator(real_images).squeeze()   
    D_real_loss = criterion(D_real_Decision,real_labels)        
    #with fake data        
    z_ = to.randn(minibatch,100 ).view(-1, 100, 1, 1)
    z_ = Variable(z_.cuda())
    gen_images = generator(z_)        
    D_fake_decision = discriminator(gen_images).squeeze()
    D_fake_loss = criterion(D_fake_decision,fake_labels)

    ## back propagation

    D_loss = D_real_loss + D_fake_loss
    discriminator.zero_grad()
    D_loss.backward()
    opt_Disc.step()

    # train generator
    z_ = to.randn(minibatch,100 ).view(-1, 100, 1, 1)
    z_ = Variable(z_.cuda())
    gen_images = generator(z_)

    D_fake_decisions = discriminator(gen_images).squeeze()
    G_loss = criterion(D_fake_decisions,real_labels)

    discriminator.zero_grad()
    generator.zero_grad()
    G_loss.backward()
    opt_Gen.step()

we just train the discriminator on real and fake images, and then train generator on the outputs of discriminator on generated images,

So Please let me know where do we compare the distribution between training and generated distribution, and how do generator learns to mimic the training samples