text: The authors present an estimator for the mutual information (MI) based on the Donsker-Varadhan representation for the KL divergence and its generalization to arbitrary f-divergences by Ruderman et al.  While that last work introduced an estimator based on optimization over the unit ball in an RKHS,  the current work propose to use a parametric function class given by a neural network  (I'd suggest that the authors make this point more explicit,  as currently it's not totally clear what their actual contribution is and how their work compares to the prior art they cite).  The authors show that such an estimator can be used to train models with less mode-dropping in adversarial models.  The work is quite straightforward,  but improves over similar work in the GAN space by Nowozin et al. by using Ruderman's tighter variational representation instead of Nguyen's one. The paper contains many typos and grammatical errors  and the authors should do an exhaustive proof-reading.  More problematic is that, right after eq. 10, the authors mention "We show in the Appendix that OMIE has the desirable strong consistency and convergence properties".  However, the appendix doesn't contain such a proof.  Is it missing from the submitted version?  I don't think that such a consistency proof is strictly necessary for a paper like this,  but for the review to be accurate I need to see the proof.  Since I can't find it,  I assume it does not exist.  In that case, the authors should give less emphasis to the MI estimator itself and more to the empirical properties and applications. The authors present some experiments comparing different estimators of MI applied to synthetic data.  Figure 1 is hard to read,  I suggest the authors try to come up with a more legible plot.  Figure 2 is also a bit surprising,  why show error for 50 dimensions but estimates for 2 dimensions?  Since these experiments are quick to run,  it would be helpful to get more information on how the gap between the methods change as the dimensionality increases (e.g. a surface plot with d and # of iterations on the x and y axes).  Also it would be highly beneficial to compare with the method in Ruderman at al.,  so that people interested in MI estimation but who don't plan on using the estimator as part of a neural net architecture can get some idea on how the inductive bias of NNs compare to RKHS. In the caption to Fig. 3 the authors state "The OMIEGAN generator learns a distribution with a high amount of structured noise", which I find hard to understand.  Probably the authors can be a bit more precise than saying "structured noise". I would recommend dropping the Information Bottleneck section to focus on showing more convincingly the impact of OMIE in GANs.  The experiments section currently looks rushed and lacking in depth. In summary, this work provides value by introducing a (previously known) superior f-divergence variational representation to the GAN community.  The mode-collapse prevention via MI maximisation is also interesting and deserves more experimental attention to make the paper stronger.