Generative Adversarial Networks have been shown to be powerful tools for generating content resulting in them being intensively studied in recent years. Training these networks requires maximizing a generator loss and minimizing a discriminator loss, leading to a difficult saddle point problem that is slow and difficult to converge. Motivated by techniques in the registration of point clouds and the fluid flow formulation of mass transport, we investigate a new formulation that is based on strict minimization, without the need for the maximization. This formulation views the problem as a matching problem rather than an adversarial one, and thus allows us to quickly converge and obtain meaningful metrics in the optimization path.
The paper addresses the task of constructing a generative model for data using a novel optimal transport-based method. The paper proposes an alternative view of obtaining generative models by viewing the generation process as a transport problem (specifically, fluid flow mass transport) between two point clouds living in high-dimensional space. To solve the transport problem, a discretization scheme is proposed, which gives rise to a variant of point cloud registration problem, which is solved using numerical optimization. The results are provided on synthetic data and a real MNIST data. 
With generative models, and particularly generative adversarial networks (GANs) being notoriously hard to train, alternative ways of constructing generative models are needed. The paper does a good job displaying the potential optimization issues arising when training GANs, and the basic theoretical foundations used in the paper have been validated in prior work. However, with the introduction of a transport-based formulation, its respective issues may arise, that are not described in the paper. Will the optimization always converge, and if yes, to which kind of optimum? What are the requirements for the point clouds R and T? 
While the conceptual contribution is that the , the technical novelty is limited and mostly amounts to the appropriate choice of distributions in R and T and applying the discretization schemes to be able to compute the experiments. Unfortunately, the model is not studied theoretically, i.e. no description is given regarding the class of generative tasks that could be solved using the method, or the class of functions that could be learn in such a way.
The experimental evaluation demonstrates on only two simple examples the results of the work. More experiments are needed to fully understand the possibilities of the framework. 
The convergence speed is not indicated, and the efficiency of the optimization is not described. 
To summarize, I believe the paper should not be accepted in its present (early) form, as (1) more detailed theoretical insight are needed, and (2) much more computational experiments are needed to fully validate the method.