Conditional GANs (CGANs) introduce a powerful extension to the standard GAN framework by allowing you to control the kind of data the model generates. Instead of producing random outputs, CGANs use conditioning: you provide extra information — such as class labels or specific attributes — to both the generator and the discriminator. This extra information guides the generator to create samples that match the desired characteristics, and helps the discriminator to judge whether a generated sample matches its condition.

To understand how this works in practice, consider the CGAN training process. The generator receives both a random noise vector and a condition (such as a digit label), and produces a sample—say, an image of a handwritten digit. The discriminator is given both a real or generated image and the same condition, and learns to determine whether the image is real or fake for that particular condition. This setup enables controlled generation: for example, you can ask the generator to produce only images of the digit "3" by setting the condition accordingly.

The core idea is reflected in the CGAN training algorithm below:

1. For each training iteration:
   • Sample a batch of real data and their labels;
   • Sample a batch of random noise vectors;
   • Sample a batch of labels (could be the same as above or chosen at random);
   • Generate fake samples using the generator, conditioned on the noise and labels;
   • Train the discriminator on:
     • Real data with correct labels (should output "real");
     • Generated data with corresponding labels (should output "fake").
   • Train the generator to fool the discriminator, using noise and labels as input.