@Akanksha_Paul, remember from the videos that the 1-L continuity condition that we’re trying to address with the gradient penalty is a condition on the critic only.
As far as why this is the case, for me, the easiest way to think about this is to remember that the critic needs to consider both its predictions for fake images as well as its predictions for real images with the goal of pushing these distributions farther apart from each other. This is exactly the situation where we need the extra condition to encourage 1-L continuity.
The generator, on the other hand, really only needs to consider the critic’s predictions on its fake images. Its goal is to fool the critic with its fake images - the higher the value, the more real the critic thinks the generator’s image is, which is exactly what the generator wants.
If you’re interested, there’s a little more discussion about intuitive differences between WGAN generator and critic losses in this post: Why is the Generator Loss in WGAN negative mean of the predicted image
If you want to go deeper into exactly why this works the way it does, there’s a link to the official Wasserstein GAN paper here: Build Basic GANS Week 3 Works Cited