Recently, Generative Adversarial Networks (GANs) have emerged as a popular alternative for modeling complex high dimensional distributions. Most of the existing works implicitly assume that the clean samples from the target distribution are easily available. However, in many applications, this assumption is violated. In this paper, we consider the problem of learning GANs under the observation setting when the samples from target distribution are given by the superposition of two structured components. We propose two novel frameworks: denoising-GAN and demixing-GAN. The denoising-GAN assumes access to clean samples from the second component and try to learn the other distribution, whereas demixing-GAN learns the distribution of the components at the same time. Through comprehensive numerical experiments, we demonstrate that proposed frameworks can generate clean samples from unknown distributions, and provide competitive performance in tasks such as denoising, demixing, and compressive sensing.
Quality is good, just a handful of typos.
Claritys above average in explaining the problem setting.
Originality: scan refs...
Significance: medium
Pros: the authors develop a novel GAN-based approach to denoising, demixing, and in the process train generators for the various components (not just inference). Further, for inference, the authors propose an explicit procedure. It seems like a noveel approach to demixing which is exciting.
Cons: The experiments do not push the limits of their method. It's difficult to judge the demixing 'power' of the method because it's difficult to tell how hard the problem is. Their method seems to easily solve it (super low MSE). The classification measure is clearly improved by denoising, which is totally unsurprising-- There should definitely be comparison with other denoising methods.
In general, they don't compare to any other methods. Actually in the appendix, comparisons are provided for a basic compressive sensing problem, but their only comparator is "LASSO" with a "fixed regularization parameter", and vanilla GAN. Since the authors "main contribution" (their words) is demixing, I'm surprised that they did not compare with other demixing approaches, or try on a harder problem. Could you  give some more details about the LASSO approach? How did you choose the L1 parameter?
I have another problem with the demixing experimental setting. On one hand, both the sinusoids and MNIST have "similar characteristics" in the sense that they are both pretty sparse, basically simple combinations of primary curves. This actually makes the problem harder for a dictionary learning approach like MCA (referenced in your paper). On the other hand, both signals are very simple to reconstruct. For example, what if you superimposed the grid of digits onto a natural image? Would you be able to train the higher resolution GAN to handle a more difficult setting? The other demixing setting of adding 1's and 2's has a similar problem.
The authors need to provide (R)MSE  results that show how well the method can reconstruct mixture components on average over the dataset. The only comparison is visual, and no comparators are provided.
Conclusions:
I'm actually torn on this paper. On one hand this paper seems novel and clearly contributes to the field. On the other hand, HOW MUCH contribution is not addressed experimentally, i.e. the method is not properly compared with other denoising or demixing methods, and definitely not pushed to its limits. It's hard to assess the difficulty of the denoising problem because their method does so well, and it's hard to assess the difficulty of demixing because of the lack of comparators.
Caveats:
I am knowledgeable about iterative optimization approaches to denoising and demixing, especially MCA (morphological component analysis), but *not knowledgeable about GAN-based approaches*, though I have familiarity with GANs.
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Update after author response:
I think the Fashion-MNIST experiments and comparisons with ICA are many times more compelling than the original experiments. I think this is an exciting contribution to dually learning component manifolds for demixing.