Paper:
State-of-the-art deep learning methods for outlier detection make the assumption that outliers will appear far away from inlier data in the latent space produced by distribution mapping deep networks. However, this assumption fails in practice, because the divergence penalty adopted for this purpose encourages mapping outliers into the same high-probability regions as inliers. To overcome this shortcoming, we introduce a novel deep learning outlier detection method, called Outlier Preserving Distribution Mapping Autoencoder (OP-DMA), which succeeds to map outliers to low probability regions in the latent space of an autoencoder. For this we leverage the insight that outliers are likely to have a higher reconstruction error than inliers. We thus achieve outlier-preserving distribution mapping through weighting the reconstruction error of individual points by the value of a multivariate Gaussian probability density function evaluated at those points. This weighting implies that outliers will result in an overall penalty if they are mapped to low-probability regions. We show that if the global minimum of our newly proposed loss function is achieved, then our OP-DMA maps inliers to regions with a Mahalanobis distance less than δ, and outliers to regions past this δ, δ being the inverse Chi Squared CDF evaluated at 1 − α with α the percentage of outliers in the dataset. Our experiments confirm that OP-DMA consistently outperforms the state-of-art methods on a rich variety of outlier detection benchmark datasets.

Review:
This work proposes an outlier detection method based on WAE framework. WAE is trained to ensure that 1) latent distribution follows a prior distribution 2) weighted reconstruction error is low where prior PDF is used to weight the reconstruction error.
Positives
------------
1.I liked the intuition behind the proposed method and I felt its worth exploring. Paper points out that in previous works, there is no mechanism to prevent outliers from getting mapped to high probability areas in the model [21]. Authors claim that their method will over-come this issue. I believe this is the core contribution of the paper.
2.I agree with authors point that WAE is a better choice than VAE for outlier detection because, former "encourages the latent representations as a whole to match the prior ". 
3.I agree training with a distributional divergence loss along with a weighed reconstruction loss will be helpful for learning a robust representation (as outliers in the training dataset would be assigned a lower weight). 
4.Authors have compared the performance of their method on OOD dataset where they have  compared against three other baseline methods, where they obtain better performance in majority of cases.
Negatives
--------------
A. Outlier detection and anomaly/novelty detection are two very different problems.  Outliers are 'bad eggs' coming from the same class as normal data. On the other hand, anomaly/novelty are unexpected data possibly coming from other classes. This is the taxonomy followed by majority of works. In my understanding this work is about 'outlier detection'. I hope authors will use the term 'outlier detection' consistency through the paper.
B. Authors have not done a good survey on existing outlier detection methods.  Eg:
    I. Chong You, Rene Vidal, Provable Self-Representation Based Outlier Detection in a Union of Subspaces, CVPR 17
    II. Yan Xia, Xudong Cao, Fang Wen, Gang Hua, Jian Sun, Learning Discriminative Reconstructions for Unsupervised Outlier Removal, ICCV 15
   III. Mohammad Sabokrou, Mohammad Khalooei, Mahmood Fathy, Ehsan Adeli, Adversarially Learned One-Class Classifier for Novelty Detection, CVPR 18. (they have experiments on outlier detection)
C. Although existing methods have not explicitly stated the problem identified in (1) above, their proposals are indirectly solving this problem. Therefore, authors should have compared with papers listed in (B) to demonstrate the effectiveness of their method for a meaningful comparison.
D. This is the first time I'm seeing the OOD dataset used in the paper. Have other works published their results on this dataset? Can they be included in your paper?. If not, consider reporting results on standard datasets used in papers (B). I believe reporting results on at least two datasets is necessary to demonstrate the generalizability of the method.
Other comments
------------------------
a. What is the dimensionality used in the latent space? I believe a larger latent space may be required in modeling more complex data such as images. Is the weighting mechanism effective when a very large latent space is used due to the curse of dimensionality. 
b. I don't think the synthetic dataset experiment is giving any interesting insights. This space is better used if an additional dataset is used instead.
In conclusion, I like the idea presented in this paper; however, I believe experimental results needs to be improved significantly to demonstrate the effectiveness of the proposed method. I cannot recommend to accept the paper in its present condition. 
Post Rebuttal:
Authors have partially addressed my concerns. In light of new experiments provided, I'm changing my decision to weak accept.