Generative Adversarial Networks (GANs) have been impactful on many problems and applications but suffer from unstable training. Wasserstein GAN (WGAN) leverages the Wasserstein distance to avoid the caveats in the minmax two-player training of GANs but has other defects such as mode collapse and lack of metric to detect the convergence. We introduce a novel inference WGAN (iWGAN) model, which is a principled framework to fuse auto-encoders and WGANs. The iWGAN jointly learns an encoder network and a generative network using an iterative primal dual optimization process. We establish the generalization error bound of iWGANs. We further provide a rigorous probabilistic interpretation of our model under the framework of maximum likelihood estimation. The iWGAN, with a clear stopping criteria, has many advantages over other autoencoder GANs. The empirical experiments show that our model greatly mitigates the symptom of mode collapse, speeds up the convergence, and is able to provide a measurement of quality check for each individual sample. We illustrate the ability of iWGANs by obtaining a competitive and stable performance with state-of-the-art for benchmark datasets.
In this paper, an inference WGAN model (iWGAN) is proposed that fuses autoencoders and WGANs. By working on both the prime and dual problems, the proposed iWGAN takes an objective that is in general the upper bound of WGAN. The generalization error bound of iWGAN is analysed and its probabilistic interpretation under maximum likelihood estimation is provided.  The proposed iWGAN model is validated on both synthetic and real (MNIST and CelebA) datasets. 
Pros:
This paper not only proposed the iWGAN model, but also provided some theoretical analysis about the iWGAN, such as the generalization error bound and the probabilistic interpretation. 
Through the experiment, it seems that the proposed iWGAN works.  Especially, on the synthetic dataset, iWGAN seems to  have less mode collapse than WGAN.
Cons:
The major concerns of this paper lie in its experiment.  
(1)	There is no quantitative comparison between iWGAN and WGAN, especially on the two real image datasets.  There are only some visual examples of the results in either the main body of the text or the appendix. 
(2)	The proposed iWAN is only compared with WGAN.  There is no experimental comparison with other autoencoder GANs  in the literature,  although the paper stated that iWGAN has many advantages over other autoencoder GANs (in the abstract).
In addition to experiment, other concerns include:
(1)	The proposed method needs to be better motivated, although it is interpreted under the framework of maximum likelihood estimation. For example, what is the advantage to optimize the proposed upper bound of WGAN over its original objective? In the experiment, it seems iWGAN has less mode collapse than WGAN based on the synthetic data. But there is no explanation or discussion about why iWGAN could enjoy this favourable property.
(2)	The proposed framework is tightly based on WGAN. It is not clear whether it could be extended to other GANs, which limits the significance of the proposed work.
Due to the above concerns, rating is recommended as "3 Weak Reject."
Suggestions:  The authors are encouraged to provide extensive comparison with other autoencoder GANs and WGAN, especially in quantitative way.