Paper:
Recent studies have made tremendous progress in style transfer for specific domains, e.g., artistic, semantic and photo-realistic. However, existing approaches have limited flexibility in extending to other domains, as different style representations are often specific to particular domains. This also limits the stylistic quality. To address these limitations, we propose Cascade Style Transfer, a simple yet effective framework that can improve the quality and flexibility of style transfer by combining multiple existing approaches directly. Our cascade framework contains two architectures, i.e., Serial Style Transfer (SST) and Parallel Style Transfer (PST). The SST takes the stylized output of one method as the input content of the others. This could help improve the stylistic quality. The PST uses a shared backbone and a loss module to optimize the loss functions of different methods in parallel. This could help improve the quality and flexibility, and guide us to find domain-independent approaches. Our experiments are conducted on three major style transfer domains: artistic, semantic and photo-realistic. In all these domains, our methods have shown superiority over the state-of-the-art methods.

Review:
Summary:
In this study, the authors propose a new method for performing artistic style transfer for  arbitrary image and styles. The new method employs a cascade/serial architecture for performing the style transfer. The authors test their method using human preference studies.
In summary, I found the architecture choice to be minimally explored. More importantly, a vast majority of the results to demonstrate the relative merits of this method were qualitative. The minimal quantitative results were unconvincing and left many unanswered questions about how well one could trust these results.
Major Comments:
1. No experiments to explore the architecture hyperparameters.
A natural question might be how the quality of the method varies systematically as the number of methods N grows. Presumably, if N=1, this would recover previous methods. 
2. Authors are missing an important reference and point of comparison for arbitrary style transfer.
  Exploring the structure of a real-time, arbitrary neural artistic stylization network
  Golnaz Ghiasi, Honglak Lee, Manjunath Kudlur, Vincent Dumoulin, Jonathon Shlens
  https://arxiv.org/abs/1705.06830
  http://goo.gle/2oiDKaT 
3. Minimal quantitative analysis.
A vast majority of the results (30 of 32 figures) are qualitative comparisons and the paper is sorely lacking an emphasis on quantitative comparisons. This is a large and notable problem in this paper and a quantitative comparison *should* constitute the primary thrust and central result of such a paper to convincingly demonstrate to a reader that the proposed method is indeed to superior to other techniques. I wish the authors dedicated more emphasis in this paper to a detailed quantitative comparison for these methods. As a starter, the analysis presented as the final two appendix figures (31 and 32) should be front and center in the result section of the paper.
4. User study for quantitative comparison is incomplete and unconvincing.
Table 1 and Appendix Figure 31 and 32 represent the primary result of this paper as these results and comprise the user studies to quantify how much better this method is to previous methods. These studies however are fairly unconvincing as lots of details are omitted and and I am concerned about the rigor of the human studies including but not limited to:
  4a. How long did each human study each image? What controls were added to the study to ensure that all images were equally studied by humans? For instance, were any golden tests employed to ensure user engagement throughout the study?
  4b. What was the repeatability of each measurement of preference? If a single human was presented the same image twice, how consistent were there ratings? For that matter, how consistent were the ratings across humans? I presume that some humans preferred some styles over others but how systematic was this?
  4c. What types of user testing scenarios were explored to ensure minimal bias in the results? Were multi-choice, paired choice or force choice employed? What about minimal or maximal time limit enforcement?
  4d. How can I have confidence that the authors did not cherry pick images and styles that favored their method? For that matter, I would expect that some methods work better on some styles or images. I would expect to see analysis accordingly to break down which styles/images work better on different slices of the data.
  4e. The statistical significance of Figure 31 and Figure 32 is not provided. What would an error bar look like with resampling?