Generative adversarial networks (GANs) learn to map samples from a noise distribution to a chosen data distribution. Recent work has demonstrated that GANs are consequently sensitive to, and limited by, the shape of the noise distribution. For example, a single generator struggles to map continuous noise (e.g. a uniform distribution) to discontinuous output (e.g. separate Gaussians) or complex output (e.g. intersecting parabolas). We address this problem by learning to generate from multiple models such that the generator's output is actually the combination of several distinct networks. We contribute a novel formulation of multi-generator models where we learn a prior over the generators conditioned on the noise, parameterized by a neural network. Thus, this network not only learns the optimal rate to sample from each generator but also optimally shapes the noise received by each generator. The resulting Noise Prior GAN (NPGAN) achieves expressivity and flexibility that surpasses both single generator models and previous multigenerator models.
Overall:
IIUC, the main contribution of this paper is to take previous work on training GANs with
multiple generators and add a learned assignment of z -> G_i, so that we have
G(z) = \sum_i NP(G_i | z) * G_i(z)
where NP is this learned assignment.
I think that technically this idea is new,
but there is important related work [1] that (IMO)
  - does essentially the same thing
  - better experimentally validates the thing they do
  - was published in last ICLR.
I also have a number of issues with the experimental design: see my detailed comments below.
Finally, the technique seems like it can't easily scale up to larger GANs or data sets 
because it requires instantiating many copies of the generator in memory?
For these reasons, I lean somewhat strongly toward rejection.
Detailed comments on draft:
It's worth noting that conditional GANs also sample from multiple disconnected `manifolds'.
I guess the value of adding your technique is that it can work without labels?
> Our approach differs significantly from those previously
strange sentence.
>  By dividing up the space into four slices...
I don't get this part. 
If you fed all the slices to a single generator you could
generate four `disconnected manifolds' with just 1 generator, no?
> , multiple-discriminator mixture in (Arora et al., 2017)
Nit: you don't need the parens there, IMO.
> our model learns to model the data over the full collection of generators in each minibatch
Given that modern GAN techniques (e.g. bigGAN), this is going to have some pretty unpleasant
performance characteristics, right?
Each generator has to be instantiated in memory all the time.
> LGAN
Nit: surely, given the state of the GAN literature, this name has been used before.
> We compare our NPGAN’s ability to model this distribution to
The following baseline seems like it would be much simpler and get the job done:
Train a GAN on a prior that's a mixture of like 100 gaussians or whatever. 
Then it seems like it could learn to assign 70, 50, and 30 of those modes
to each one of the gaussians in your underlying data?
I guess I haven't tried this myself, but it seems like a more fair comparison.
The way the current experiment is set up, you know a priori that your model
is the only one that can work.
Overall, I don't really understand why it's necessary to have multiple generators.
If I want the prior my generator `sees' to be disconnected, can't I just
pass samples from the prior through a standard relu network?
Surely a relu network can learn to separate one mode into two, and so forth.
But once you do that, you've essentially got [1].
> We next demonstrate
Would be nice to have a new subesection here.
I think your single-generator baseline in Fig 2 and 3 is unrealistically bad.
See fig 3 of [2], in which it looks bad but not nearly as bad as you've shown it.
I think this points to another issue with the experimental design.
If the generator is a big enough relu network, it ought to be able to automatically
generate `disconnected bits', but it has to be big enough, and you've compared a
generator with N parameters to 2 and 3 generators with N parameters each.
Moreover, your learned noise prior has some extra number of parameters (I don't see
where you described these but I may be missing it).
> A single generator is unable to model this non-disconnected data.
Again, I have a feeling that this is because of the small generator you use.
I'm pretty sure that a motivated person could get a normal GAN to model the
distribution in fig 5 reasonably well.
> The other models can only work if the precise optimal number of generators is known a
priori.
Isn't this not true for the method that throws out redundant generators?
The experiments described in 4.3 and 4.4 are pretty contrived.
It's ok to have some contrived experiments, but it seems like all experiments
on which you were able to provide evidence that your technique was helpful are contrived.
It also seems like the baselines you used are not obviously the right choice for these
experiments?
Re: your CIFAR experiments:
I think this supports my earlier claim that the extra parameters and bells and whistles
in modern GAN techniques *already implicitly do what your method is proposing to do*.
I think a lot of people miss this point when writing papers about GANs.
When people request comparisons against more modern techniques,
they're not (merely) being difficult: 
they want to know if the technique you propose "stacks" with other techniques,
in the sense that your method is doing something that wasn't already being done implicitly
by the old methods.
References:
[1] On Self Modulation for Generative Adversarial Networks (https://arxiv.org/abs/1810.01365)
[2] Discriminator Rejection Sampling (https://arxiv.org/pdf/1810.06758.pdf)