# What is the reason for mode collapse in GAN as opposed to WGAN?

$$D_{KL}$$ gives us inifity when two distributions are disjoint. The value of $$D_{JS}$$ has sudden jump, not differentiable at $$\theta=0$$. Only Wasserstein metric provides a smooth measure, which is super helpful for a stable learning process using gradient descents.

Why is this important for a stable learning process? I have also the feeling this is also the reason for mode collapse in GANs, but I am not sure.

The Wasserstein GAN paper also talks about it obviously, but I think I am missing a point. Does it say JS does not provide a usable gradient? What exactly does that mean?

Looking at Figure 1 from the WGAN paper, we clear see that the JS divergence on the right is not continuous at $$0$$, hence not differentiable at $$0$$. However, the EM plot on the left is continuous also at $$0$$. You could now argue that we have a kink there, so it should not be differentiable there either, but they might have a different notion of differentiability, I am honestly not sure about it right now.