To train flow based models, you usually either use forward or reverse kl as your loss function. My question is, can you use wasserstein distance directly as your loss function to replace kl? I have used other f-divergences in place of kl before, but have never seen anyone use this distance metric before. There is one paper (Riemannian Normalizing Flow on Variational Wasserstein Autoencoder for Text Modeling) kinda addressing this but as far as I can tell it doesn't directly answer this question.

  • $\begingroup$ Sure you can. (P.S. You can link to and give the title of the peer reviewed version, instead of the arXiv preprint.) $\endgroup$ May 14 at 20:42
  • $\begingroup$ Good tip, will edit my question. I'm mostly wondering how come it's not a common theme in these types of GMs? I mean with GANs it's widely used, but with flow based models I've rarely seen integral probability based losses such as Wasserstein being used $\endgroup$
    – Saam
    May 15 at 5:49
  • $\begingroup$ Feel free to edit whenever. $\endgroup$ May 15 at 16:47


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