text: The article "Do GANs Learn the Distribution? Some Theory and Empirics" considers the important problem of quantifying whether the distributions obtained from generative adversarial networks come close to the actual distribution of images. The authors argue that GANs in fact generate the distributions with fairly low support. The proposed approach relies on so-called birthday paradox which allows to estimate the number of objects in the support by counting number of matching (or very similar) pairs in the generated sample. This test is expected to experimentally support the previous theoretical analysis by Arora et al. (2017). The further theoretical analysis is also performed showing that for encoder-decoder GAN architectures the distributions with low support can be very close to the optimum of the specific (BiGAN) objective. The experimental part of the paper considers the CelebA and CIFAR-10 datasets. We definitely see many very similar images in fairly small sample generated. So, the general claim is supported. However, if you look closely at some pictures, you can see that they are very different though reported as similar. For example, some deer or truck pictures. That's why I would recommend to reevaluate the results visually, which may lead to some change in the number of near duplicates and consequently the final support estimates. To sum up, I think that the general idea looks very natural and the results are supportive. On theoretical side, the results seem fair (though I didn't check the proofs) and, being partly based on the previous results of Arora et al. (2017), clearly make a step further.