Computing equilibrium states for many-body systems, such as molecules, is a long-standing challenge. In the absence of methods for generating statistically independent samples, great computational effort is invested in simulating these systems using, for example, Markov chain Monte Carlo. We present a probabilistic model that generates such samples for molecules from their graph representations. Our model learns a low-dimensional manifold that preserves the geometry of local atomic neighborhoods through a principled learning representation that is based on Euclidean distance geometry. In a new benchmark for molecular conformation generation, we show experimentally that our generative model achieves state-ofthe-art accuracy. Finally, we show how to use our model as a proposal distribution in an importance sampling scheme to compute molecular properties.
In this paper, a new method for estimating the equilibrium measure of molecular compounds is proposed and tested on a new (enriched) version of an existing data set (CONF17 is derived from the pre-existing ISO17, itself extracted from QM9). 
The method takes as input a collection of graph structures of a given stoichiometry mixture, and learns the corresponding conformations.
This results in a generative model, taking as input a graph structure (or actually a single conformation instance, thus setting the stoichiometry AND the isomer/graph structure), to generate (in a one-shot fashion) other conformations of that isomer.
The distribution of conformations sampled in this way compare well with those of an extensive training set (CONF17, set of isomers and conformations of a single compound), and in particular they perform better than 2 alternative methods published recently (2015 and 2019, the former performing globally much better than the latter!).
Concretely, the model/method/algorithm consists in a combination of existing network architectures.  The main original contribution is to map the Cartesian coordinates of atoms into a pairwise distance space, which is naturally translationally and rotationally invariant.  Some of the second and third neighbors distances in the graph structure are considered, such that the conformation is completely set (this would not be the case if considering only 1st nearest neighbors distances).
The precise combination of architectures is explained in section 2.2. This explanation is a little fast for me (but I am new to this field). 
In that section, it could be nice to precise that the job of the CVAE is to learn (among others) the parameters mu,sigma of q_phi(z|d,G), using a batch of conformations of a given isomer (and then generalize to other isomers, each time guessing the correct mu,sigma parameters, even for a new isomer).
This is not obvious for the inexperienced reader (I hope I "guessed" correctly).
The "new dataset" shared in this work is indeed useful for reproducing results and for later comparison with other works which aim at sampling conformations.
However, it derives directly from ISO17, which is itself an extraction from QM9. ISO17 lists the Cartesian coordinates of 127 isomers of C7,H10,O2 (each having ~3000 conformations).  The "new" CONF17 is novel only in that it provides these conformations in distance-matrix space, i.e. it sets which pairs of atoms need to have their distances computed.  This is very useful because this choice of pairs is not unique, and so setting it once is necessary for comparison.  I would not stress too much that this is a new dataset: at first it actually sounds like authors chose a dataset such that their method outperforms others'!  Which turns out not to be the case (they chose C7,H10,O2, but this doesn't look like fine-tuning).  Indeed, their sharing of this augmented version of ISO17 is absolutely necessary: I would simply put it differently, stating from the beginning that they share an augmented version of a pre-existing data set.
About the experimental protocol/methodology:
the work carried out seems quite impressive. Indeed, the paper presents a rather extensive comparison of the new model with 2 other ones, on a large data set.
However sometimes the presentation rushes a bit towards results, in the sense that it is not easy to figure out over which ensemble the mean/median/max/min has been computed. This is related to the intrinsic complexity of estimating accuracy, given the encapsulation (compound-> isomer-> conformations-> each bond-> distribution over bond properties).  I think however it could be made clearer, and this would benefit the paper greatly.
A deeper comment: in the field of conformation sampling, there are two issues. One is to correctly sample states in each local minimum of the free energy. This is addressed in the paper. The second issue is to hunt for all possible local minima of the isomer, i.e. sample even unlikely but crucial conformations. This is not addressed here.  For computing average energy, dipole moment etc, the most likely conformations will dominate, most of the time.  However given the topic I think it would be fair to mention this point, and explain why in this specific case, the second issue is not crucial.
Because of this, also, I think 
Overall, the paper is well written and is very well situated within the literature (including the very recent literature).
It states clearly its contributions and results, and provides detailed presentation of experimental results.
I think it contributes to the field and provides an interesting new way of dealing with the problem of molecular conformations sampling.  The results obtained are much better than those of the compared ML method (RDkit).
However, some claims (in introduction or in section 3) are stated more strongly than they are supported by direct experimental evidence.
- ''... the first work on sampling molecular conformations for molecules of arbitrary size and shape based on deep learning.''
However, the experiments have been performed only on isomers of  C7,H10,O2.
Furthermore, there is no discussion on the computational cost of the method at all, so its extendibility to larger shapes is not obvious.
- '' We create a new, challenging benchmark dataset CONF 17 for conformation generation, which is made publicly available.''
I made remarks on this claim above.'' 
- '' We develop a rigorous experimental approach for evaluating and comparing the accuracy of conformation generation methods based on the mean maximum deviation distance metric.''
However the paper's methodology doesn't address the issue of ''hunting for new local minima''. 
The data set could be enriched also with a labeling of ''which conformation is in which local minimum of free energy''
- ''It is a fast alternative to resource-intensive approaches based on MCMC or MD.''
As there was no mention of speed of computation in the paper (although we can guess it is faster), this is unsupported. However it is easy to remedy, simply give an order of magnitude of sampling time (for thousands of conformations of 1 isomer).
- ''Our principled representation based on pair-wise distances does not restrict our approach to any type of system (e.g., proteins) or any particular graph structure. In addition, it is extendable in a systematic fashion.''
This suggests that the method would also work for dense packings. However this is not shown in the experiments.
Probably I misunderstood the claim, and it only refers to the ability to tackle general molecular compounds, not just linear ones?  However proteins are not always linear, but can present cycles, and other branch-style patterns, so the claim is not very clear to me.
Because some of the important claims are only weakly supported, and because of the relatively small novelty of the method, I lean on rejecting the paper.
Additional comments (for improving the paper):
There is no discussion of hyper-parameter tuning, or any detail of the intermediate GNN that constitute the encoder and decoder in the CVAE. 
So it was either not done at all, and then it should be mentioned; or it was done and it should be discussed quickly.
In particular, in section 2.2 there is no discussion on the impact of the latent space' dimension, here set to Nv, i.e. 7+2+10=19 (correct?).  I guess there is a balance between accuracy and generalizability, a short discussion on this point would be interesting.
The paper should clarify the hierarchy of molecular configurations:
for a given composition (%C, %O, %H, etc) (here, fixed throughout the paper at C7,H10,O2)
there are several structures possible (graphs or isomers),
for a given graph (isomer), there can be a couple of chiral variants (mirroring of (pieces of) the molecule,
for each chiral variant, there are conformations, which correspond to rather weak variations of the Cartesian coordinates, due to thermal fluctuations. Some of these variations can be important, e.g. when a bond can freely rotate. Some correspond to bending or torsion, etc, of the molecule.
The algorithm presented in the paper attempts to sample appropriately the equilibrium distribution of conformations for each given graph structure (at fixed chirality, if I understood correctly).
Add a comment on why (in your opinion) the distributions are not exactly correctly sampled, which after all is the goal (since the initial graph structure is given as input here).
Additional question, for curiosity. In section 2.3: only a single molecule output is taken from each distance matrix.
Could you comment on the possibility to sample several Cartesian coordinates, for each distance matrix ?  It seems like several solutions should (often) exist. 
Sampling continuously from that distribution would surely provide a more continuous (rich) output (am I correct) ?