WGAN loss diverges

I have some trouble to understand the WGAN Loss values.

I understand that we do not have a discriminator anymore, but a critic. Difference is, that the Discriminator tries to classify the input ergo map it to either 0 or 1 and that the critic tries to score them. The scoring map to any real number and the Loss function is:

L_critic = Critic(fake_input) - Critic(real_input) + weight * gradient_penalty

And the Loss function for the generator which produces the fake_input is:

L_generator = - Critic(fake_input)

My question is: Over the Epochs my Loss values for the generator and Discriminator diverges and takes really high numbers. Is this common? I have seen elsewhere that the Loss of the Critic drop to 0, but what ensures that? As far as I understood the Critic tries to score the real from fake as far apart as possible.

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