Paper:
Semi-supervised learning approaches based on generative models have now encountered 3 challenges: (1) The two-stage training strategy is not robust. (2) Good semi-supervised learning results and good generative performance can not be obtained at the same time. (3) Even at the expense of sacrificing generative performance, the semi-supervised classification results are still not satisfactory. To address these problems, we propose One-stage Semi-suPervised Optimal Transport VAE (OSPOT-VAE), a one-stage deep generative model that theoretically unifies the generation and classification loss in one ELBO framework and achieves a tighter ELBO by applying the optimal transport scheme to the distribution of latent variables. We show that with tighter ELBO, our OSPOT-VAE surpasses the best semi-supervised generative models by a large margin across many benchmark datasets. For example, we reduce the error rate from 14.41% to 6.11% on Cifar-10 with 4k labels and achieve state-of-the-art performance with 25.30% on Cifar-100 with 10k labels. We also demonstrate that good generative models and semi-supervised results can be achieved simultaneously by OSPOT-VAE.

Review:
Contributions:
The main contribution of this paper lies in the proposed OSPOT-VAE for semi-supervised classification. The proposed model is (i) an one-stage framework that unifies the generation and classification loss in one ELBO, (ii) achieves a tighter ELBO by applying optimal transport to the distribution of the latent variables, and (iii) achieves SOTA semi-supervised learning results without sacrificing generative performance on many benchmarks. 
Strengths:
(1) Novelty: This paper contains novelty in terms of two aspects. First, the derivation of Eqn. (13) unifies both generation loss and classification loss naturally. The derivation seems different from a standard semi-supervised VAE. Second, the use of optimal transport (OT) estimation to tighten the ELBO results in improved classification performance. The use of OT seems novel in this context. 
(2) Writing: The paper is generally well written. However, I also found section 3 is hard to follow, with details in the Weaknesses section.
(3) Experiments: The results look impressive. OSPOT-VAE achieves better performance than other generative approaches. 
Weaknesses:
(1) Clarity: My biggest concern lies in the clarity of section 3, which I think is confusing in its current shape. After several rounds of reading, below is my understanding. In section 3.1, the authors first derive the objective in Eqn. (13). This objective is derived based on the use of mutual information (Eqn. (8)). By the end, no special cross-entropy loss term like in Eqn. (7) is needed.  Second, in order to tighten the bound, section 3.2 introduces optimal transport estimation. Combining these two losses together (see in Algorithm 2) results in the final algorithm. However, generally, I feel the presentation of section 3 is confusing. One may need to present the big picture (framework) first, and then dig into details.
Besides that, I have some questions as below. 
a) There are many hyper-parameters in the final objective, for example, the mutual information I_z, I_c is also considered as hyper-parameters. How all these hyper-parameters are selected?
b) Is there any intuition on why Eqn. (13) is already enough without introducing the empirical cross-entropy loss like in Eqn. (7)? It seems to me adding this additional cross-entropy loss will not hurt performance. 
c) In Eqn. (12), how is the last term D_{KL}(p(c|X)||q_{\phi}(c|X)) calculated, since we cannot get the true p(c|X)?
d) As shown in Table 4, the use of optimal transport seems to be the key. However, section 3.2 is hard to follow. For example, In Algorithm 1, Line 6 & 7 considers the true posterior of z and c is a Gaussian and a multinomial distribution, respectively. Why doing this? Supported by theory? I also feel the calculation of L_{Rz} and L_{Rc} in Line 8 & 9 is hard to follow. 
e) How reliable is this optimal transport estimation is? And how it contributes to the final classification performance? Since this loss term is not a classification loss, then is there any intuition on why it serves as a regularization to help the final performance so much?
f) Results in Table 5 on Cifar10 seem not imply OSPOT-VAE tightens the ELBO. Adding results on MNIST will be better, since the ELBO on MNIST is widely benchmarked. 
(2) Minor:
a) I am not sure why section 2.1 is needed. Also, the feature matching GAN paragraph in section 2.2 seems also unnecessary. If you really want to discuss the use of GAN for semi-supervised learning, then there is a lot of other work that needs discussion.
b) There is a missing right bracket in the second term of Eqn. (9).
Overall, I think the results look quite impressive. However, the presentation of the method part is unclear to me, and could be much improved.