text: The authors propose a new regularization term modifying the VAE (Kingma et al 2013) objective to encourage learning disentangling representations. Specifically, the authors suggest to add penalization to ELBO in the form of -KL(q(z)||p(z)) , which encourages a more global criterion than the local ELBOs. In practice, the authors decide that the objective they want to optimize is unwieldy and resort to moment matching of covariances of q(z) and p(z) via gradient descent. The final objective uses a persistent estimate of the covariance matrix of q and upgrades it at each mini-batch to perform learning. The authors use this objective function to perform experiments measuring disentanglement and find minor benefits compared to other objectives in quantitative terms. Comments: 1. The originally proposed modification in Equation (4) appears to be rigorous and as far as I can tell still poses a lower bound to log(p(x)). The proof could use the result posed earlier: KL(q(z)||p(z)) is smaller than E_x KL(q(z|x)||p(z|x)). 2. The proposed moment matching scheme performing decorrelation resembles approaches for variational PCA and especially independent component analysis. The relationship to these techniques is not discussed adequately. In addition, this paper could really benefit from an empirical figure of the marginal statistics of z under the different regularizers in order to establish what type of structure is being imposed here and what it results in. 3. The resulting regularizer with the decorrelation terms could be studied as a modeling choice. In the probabilistic sense, regularizers can be seen as structural and prior assumptions on variables. As it stands, it is unnecessarily vague which assumptions this extra regularizer is making on variables. 4. Why is using the objective in Equation (4) not tried and tested and compared to? It could be thought that subsampling would be enough to evaluate this extra KL term without any need for additional variational parameters \psi. The reason for switching to the moment matching scheme seems not well motivated here without showing explicitly that Eq (4) has problems. 5. The model seems to be making on minor progress in its stated goal, disentanglement. It would be more convincing to clarify the structural properties of this regularizer in a statistical sense more clearly given that experimentally it seems to only have a minor effect. 6. Is there a relationship to NICE (Laurent Dinh et al)? 7. The infogan is also an obvious point of reference and comparison here. 8. The authors claim that there are no models which can combine GANs with inference in a satisfactory way, which is obviously not accurate nowadays given the progress on literature combining GANs and variational inference. All in all I find this paper interesting but would hope that a more careful technical justification and derivation of the model would be presented given that it seems to not be an empirically overwhelming change.