How exactly do you backpropagate the gradient penalty in WGAN-GP?

Question

I am trying to implement WGANs from scratch. The loss function for the critic is given by :

which i implement in my code as L = average(real output) - average(fake output) + lambda*GP.

For calculating GP, i just backpropagated ones in the critic to get gradient w.r.t interpolated images, and did (l2_norm(gradient)-1)^2.

I understand that pytorch and tensorflow have some sort of automatic differentiation to calculate the gradients of the loss function. However, I am trying to manually backpropagate the gradient of the loss function.

For vanilla WGAN, the gradient that i backpropagate is -1/n for real images and +1/n for fake images. But I am having trouble understanding how to calculate the gradient of the loss function taking into account gradient penalty.

**How exactly do you apply gradient penalty after calculating it? What exactly should you backpropagate? **

Is there a different way to implement this by hand without using automatic differentiation? Or am i misunderstanding something? Any help is appreciated.

Edit: according to this repo, the training of the critic happens like this :

                # Train with real images
            d_loss_real = self.D(images)
            d_loss_real = d_loss_real.mean()
            d_loss_real.backward(mone)
        # Train with fake images
        z = self.get_torch_variable(torch.randn(self.batch_size, 100, 1, 1))

        fake_images = self.G(z)
        d_loss_fake = self.D(fake_images)
        d_loss_fake = d_loss_fake.mean()
        d_loss_fake.backward(one)

        # Train with gradient penalty
        gradient_penalty = self.calculate_gradient_penalty(images.data, fake_images.data)
        gradient_penalty.backward()

But, what exactly is happening in gradient_penalty.backward() ?

How exactly do you backpropagate the gradient penalty in WGAN-GP?

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