Generative Adversarial Networks (GANs) have shown impressive results in modeling distributions over complicated manifolds such as those of natural images. However, GANs often suffer from mode collapse, which means they are prone to characterize only a single or a few modes of the data distribution. In order to address this problem, we propose a novel framework called LDMGAN. We first introduce Latent Distribution Matching (LDM) constraint which regularizes the generator by aligning distribution of generated samples with that of real samples in latent space. To make use of such latent space, we propose a regularized AutoEncoder (AE) that maps the data distribution to prior distribution in encoded space. Extensive experiments on synthetic data and real world datasets show that our proposed framework significantly improves GAN's stability and diversity.
It is argued in this paper that GANs often suffer from mode collapse, which means they are prone to characterize only a single or a few modes of the data distribution. In order to address this problem, the paper proposed a framework called LDMGAN which constrains the generator to align distribution of generated samples with that of real samples in latent space by introducing a regularized AutoEncoder that maps the data distribution to prior distribution in encoded space.
The major difference of this paper from many traditional GANs is to constrain the distributions of generated data same as distributions of true data in latent space instead of constrain the ability of discriminator. The authors detailed their motivation, the algorithm, and also reported a series of evaluation results on several datasets. 
Generally, this paper was well written. However, this paper has the following major concerns: 
	（1） Though somewhat new, the novelty of this paper may be incremental to me. It looks like a combination of VEEGAN and AAE.  Though the authors mentioned that VEEGAN autoencoded the noise vectors rather than data items, and AAE exploited the adversarial learning in the encoded space rather than using an explicit divergence,   it appears not significant to me between the proposed model and these two models. At least the authors did not  address sufficiently how significant the proposed method would be.
	 （2） The paper tested the proposed algorithm with a 2D Synthetic dataset. However, I found a lot of discrepancies in the results presented in Table 1 with other published works. The authors show 1 of mode captured on 2D Grid and 2D Ring using the VEEGAN method. However, the VEEGAN paper shows they get 24.6 and 8 on 2D Ring and 2D Grid respectively. Such discrepancies were also observed in Figure 3. These discrepancies must be explained.
	（3） In Figure 4, the authors showed the distribution of MODE scores for GAN and LDMGAN. From the figure, it seemed that LDMGAN improved the sample quality and diversity compared to GANs, but it is still prone to characterizing only a single or a few modes of the data distribution. In another word,  this may alleviate the problem but may not fully solve the problem.  Another minor point, the coordinate and legend are too small in this figure. It would be better if they become bigger.
	（4） The results of Table 4 is not convincing because the comparative methods are truly out-of-date. It would be more convincing if more latest methods can be compared with LDMGAN method. Those results reported are far lower than the state-of-the-art performance in these datasets. 
         (5) There is a mistake in the second term of equation 11, it should be ⋯〖-D〗_KL (p^* (y)||p(y))  )