you can optimize divergence between distributions using the Wasserstein metric using a reformulated GAN.
Here is our paper on that:

  
      
      arXiv.org
  
  
    

Wasserstein GAN 147

We introduce a new algorithm named WGAN, an alternative to traditional GAN
training. In this new model, we show that we can improve the stability of
learning, get rid of problems like mode collapse, and provide meaningful
learning curves useful for...


  
  
    
    
  
  


and the corresponding code (which is awfully simple):
https://github.com/martinarjovsky/WassersteinGAN 302