text: This paper studies how the variance of the discriminator affect the gradient signal provided to the generator and therefore how it might limit its ability to learn the true data distribution. The approach suggested in this paper models the output of the discriminator using a mixture of two Gaussians (one for “fake” and the other for “not fake”).  This seems like a rather crude approximation as the distribution of each “class” is likely to be multimodal.  Can the authors comment on this?  Could they extend their approach to use a mixture of multimodal distributions? The paper mentions that fixing the means of the distribution can be “problematic during optimization as the discriminator’s goal is to maximize the difference between these two means.“.  This relates to my previous comment where the distribution might not be unimodal.  In this case, shifting the mean doesn’t seem to be a good solution and might just yield to oscillations between different modes.  Can you please comment on this? Mode collapse: Can you comment on the behavior of your approach w.r.t. to mode collapse? Implementation details: How is the mean of the two Gaussians initialized?  Relation to instance noise and regularization techniques: Instance noise is a common trick being used to train GANs,  see e.g. http://www.inference.vc/instance-noise-a-trick-for-stabilising-gan-training/ This also relates to some regularization techniques, e.g. Roth et al., 2017 that provides a regularizer that amounts to convolving the densities with white Gaussian noise.  Can you please elaborate on the potential advantages of the proposed solution over these existing techniques? Comparison to existing baselines: Given that the paper addresses the stability problem, I would expect some empirical comparison to at least one or two of the stability methods cited in the introduction, e.g. Gulrajani et al., 2017 or Roth et al., 2017. Relation to Kernel MMD: Can the authors elaborate on how their method relates to approaches that replace the discriminator with MMD nets. e.g. - Training generative neural networks via Maximum Mean Discrepancy optimization, Dziugaite et al - Generative models and model criticism via optimized maximum mean discrepancy, Sutherland et al More explicitly, the variance in these methods can be controlled via the bandwidth of the kernel  and I therefore wonder what would one use a simple mixture of Gaussians instead?