Training generative models like Generative Adversarial Networks (GANs) is challenging for noisy data. A novel curriculum learning algorithm pertaining to clustering is proposed to address this issue in this paper. The curriculum construction is based on the centrality of underlying clusters in data points. The data points of high centrality takes the priority of being fed into generative models during training. To make our algorithm scalable to large-scale data, the active set is devised, in the sense that every round of training proceeds only on an active subset containing a small fraction of already trained data and the incremental data of lower centrality. Moreover, the geometric analysis is presented to interpret the necessity of cluster curriculum for generative models. The experiments on the cat and human-face data validate that our algorithm is able to learn the optimal generative models (e.g. ProGAN) with respect to specified quality metrics for noisy data. An interesting finding is that the optimal cluster curriculum is closely related to the critical point of the geometric percolation process formulated in the paper. Besides, the centrality-accuracy curve in our algorithm provides an effective way of visualizing the model state with curriculum training.
The paper states that training generative models is challenging when there are noisy data points in your training set. To address this, the authors propose to training methodology (or curricula)  where "easier" or more "relevant" points are presented first followed to the model followed by the less relevant ones. The relevance is determined used by calculating centrality on a graph constructed out of the data points. 
I lean towards rejecting the paper, primarily because 1) The authors have not provided evidence to claim the noisy data points makes training challenging or characterized anything about under how much noise the training breaks down. 2) Experimental evidence is not convincing  3) There are not of imprecise statements in the paper. 
The authors claim (without citation) that training generative models in the presence of noisy data is challenging. How much noise are we talking about? If the entire training set is very noisy, maybe we don't have any hope to learn to generate clean samples, but if it's just a little bit of noise, maybe it's fine. I also understand that when the authors use the word "noise" they don't really mean noise,  but changes in view point etc. Some convincing demonstration that such characteristics of dataset adversely affects the training of generative models will be helpful (in addition to one passing sentence in the experiment section about it).
I am not convinced by any of the experiments. More importantly, it seems like the proposed training curricula is in general valid for a lot of generative models. The experimental evidence is really not convincing. Very limited experiments is done on two datasets only using one particular GAN. To convincingly demonstrate that your training methodology is doing something non-trivial, you should show that this works on multiple generative models on multiple datasets and compare your performance (and visualize some generated samples) against just training blindly on the entire dataset. In addition to this, I don't understand the relevance of some of the results in the paper. For ex, what does Corollary 3 signify?
Some other points:
1. First para. "non-trial' -> non-trivial
2. First para: "model collapse" -> mode collapse
3. 3.2 para 2. "base set that guarantees a proper converge of generative models". What do you mean by "proper convergence"?
4. 3.2 para 2. "moderate compared to m". Again, what is moderate? 
5. Why do you use ResNet features (5.1) for distance? Why is this a reasonable or the best metric while computing your graph?
6. "We determine the parameter \alpha of the edge weight by enforcing geometric mean of the weights to be 0.8". It seems very arbitrary to me. Can you justify this choice?