Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: summary: The paper introduces a new type of equivariant normalizing flow by using the CNF framework with a modified equivariant graph NN as a dynamics function. The equivariance discussed is wrt Euclidean symmetries, which are important for physical systems. They show that their flow beats prior equivariant baselines on synthetic data. Moreover, the model is capable of transforming spacial, categorical and ordinal features simultaneously. This allows the sampling of molecular configurations with positions, atom types, and charges. 
main_review: Merits of paper
- The paper is clearly written, well organized and easy to understand. 
- They improve on previous work of Köhler et al. (2019, 2020) by utilizing equivariant graph NN as a dynamic function instead of their "Kernel Dynamics" function.
- Incorporating equivariant graph NN into the (equivariant) continuous normalizing flow framework is non-trivial and novel.
- The theory and related work are well presented. All previous work is acknowledged when necessary. 
- They compare to prior baseline of Köhler et al. (2020) and show that their model performs superior. 
- They introduce a new benchmark dataset, based on the QM9 dataset, and show that their model outperforms other non-equivariant as well as equivariant models.
- The theory of equivariant flows is heavily based on the derivation from Köhler et al. (2019, 2020) and Rezende et al. (2019), but they contribute a proof for equivalence of the Jacobian of the used subspace and the whole space.  
- They are able to sample new molecular configurations of different size with corresponding atom types and charges simultaneously. Meaning, they were (at least to some extent) able to learn the distribution of the subset of QM9 molecules with their E-NF. 
- This is a valuable contribution, sets a new baseline for molecular structure generation, and is very interesting for researchers in that area.

Criticism
- Although the training process and network architecture is outlined quite well, I could not find information about the Jacobian evaluation. This is of interest as it has proven to be a bottleneck in prior work, e.g. Köhler et al. (2020).  I would assume that some sort of approximation, such as the Hutchinson estimator, is used at least in the training process. I think this information should be included in the paper (or at least in the appendix).
- The most interesting experiment is the generation of molecules. However, their stability measure is only based on distances. I think a better metric for stability measure would be the energy of the generated molecules. In fact, it might be that far less than 5% of the generated molecules are stable considering the energy instead of the distances, as already small deviations of the distances as well as the atom types can have huge impact on the energies. This should at least be discussed in the final paper.

All in all, a good paper, especially when the energy of the generated molecules is included. 
limitations_and_societal_impact: As mentioned above, a further limitation could be that the generated molecules are unstable considering their energies. So far, this is not mentioned in the paper.
The authors adequately addressed potential negative societal impact of their work.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: The authors introduce a equivariant model for one-shot 3D molecule generation, building upon continuous time normalizing flows and equivariant graph networks. They demonstrated the utility of their approach based on several benchmark applications where they consistently outperform other flow-based models.
main_review: The proposed model present a sensible combination of existing methods, namely E(n) equivariant graph neural networks, variational dequantization and argmax flows. This enables the model to lean distributions over molecules considering positions as well as atom types. This is a clear improvement over previous related normalizing flows, which were focused on positional data.

The reported molecular generation experiments serve as a clear demonstration for the benefits of their method over other normalizing flows. However, one criticism is the strong focus on this particular class of methods  which is particularly noticeable in the final QM9 experiment. This makes it hard to evaluate how the proposed model behaves with respect to other generative approaches for 3D molecular structure, many of which have even been applied to the same dataset. Examples include iterative approaches that place atom after atom [1,2,3] as well as other one-shot approaches, either GAN- [4] or VAE-based [5]. A comparison to other methods is also made difficult by using the negative log-likelihood as primary evaluation metric. In this context, it would be worthwhile to analyze other statistics of the structures sampled in the QM9 experiment, e.g. how many of the stable molecules (which pass a valency check of choice) are training structures, test structures, or even novel structures and how many are unique? Additional measures of interest would be how the ring/atom/bond count of the generated structures compare to their distribution in QM9. One additional question would be how suitable the model is for practical applications, as the number of valid sampled molecules appear low at a first glance? Since QM9 provides relaxed structures of the molecules, one measure to consider in future experiments is the median RMSD between atomic positions of generated and relaxed structures, i.e.  how close are the sampled structures to actual equilibrium configurations (a drawback of this metric is that it is computationally intensive due to the need for quantum chemical computations).

The paper itself is well written providing a thorough description of the formal/theoretical background as well as the architecture.

On the whole, the proposed approach build upon and extends an interesting combination of machine learning approaches and represents a viable contribution with respect to one-shot generation. What remains unclear how it performs in comparison to other, non flow, generative approaches.

1 Simm, Gregor, Robert Pinsler, and José Miguel Hernández-Lobato. "Reinforcement learning for molecular design guided by quantum mechanics." International Conference on Machine Learning. PMLR, 2020.

2 Simm, Gregor NC, et al. "Symmetry-aware actor-critic for 3d molecular design." arXiv preprint arXiv:2011.12747 (2020).

3 Gebauer, N. W., Gastegger, M., & Schütt, K. T. (2019). Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules. arXiv preprint arXiv:1906.00957.

4 Hoffmann, Moritz, and Frank Noé. "Generating valid Euclidean distance matrices." arXiv preprint arXiv:1910.03131 (2019).

5 Nesterov, Vitali, Mario Wieser, and Volker Roth. "3DMolNet: a generative network for molecular structures." arXiv preprint arXiv:2010.06477 (2020).

limitations_and_societal_impact: Potential limitations and societal impact have been sufficiently addressed.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: The authors introduce a novel approach for generating data with intrinsic Euclidean symmetries. The proposed model uses recent advances in continuous normalizing flows, variational dequantization, and equivariant neural networks to construct a generative algorithm E(n)-equivariant along some modeled variables. The authors tackled many theoretical and technical problems to make the model stable and obtain desired equivariance in Euclidean space. The generative process looks as follows: first, the two groups of latent codes are sampled from the Gaussian distribution, which is rotation and reflection invariant; these samples are passed through the continuous normalizing flow guided by an Equivariant Graph Neural Networks. To force the translation equivariance, the authors propose to center the latent codes and work with (M-1) x n linear subspace. The target distribution is given by applying the variational dequantization for the sampled latent codes. The authors validate their approach on synthetic data and molecular conformations produced with DFT (density functional theory). 
main_review: **Originality:** Although all key parts are well-known, combining everything in one framework seems novel and original.

**Quality:** The authors motivate this work well, describe all important details of their method, and propperly discuss limitations and impact of their work. The experiments on molecular data are quite simple and miss several important metrics to evaluate whether the proposed method can compete with state-of-the-art approaches in drug discovery.

**Clarity:** The paper is well written and is easy to follow. The authors cover all key details of the proposed method and discuss all problems that were solved while developing the method.

**Significance:** The paper provides simple experiments that do not evaluate the practical significance of the method in real drug discovery problems. The missing standard deviation in metrics also makes it difficult to validate significance of the results.

Update: The authors clarified my concerns, I tend to keep the original score
limitations_and_societal_impact: The limitation of the work lies in the simplicity of the provided experiments on molecular data. First, important to say that model tries to solve two distinct drug discovery problems simultaneously — learn the distribution of molecular compounds [1] and model the distribution of conformational space for the molecular compounds [2]. Both of these problems have a wide variety of developed methods (including the neural-based) and a set of metrics on which the methods compete. I would recommend comparing the proposed model with the state-of-the-art model from these areas on the set of distribution learning and conformation modeling metrics.

[1] Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Models, Polykovskiy et al.
[2] Learning Neural Generative Dynamics for Molecular Conformation Generation, Xu et al.
review_title: null

Meta-review: All reviewers agree on acceptance. This work is a highly significant contribution by introducing equivariant graph neural networks into the
(equivariant) continuous normalizing flow framework to obtain invertible equivariant functions. They show that their flow beats prior equivariant baselines and allows the sampling of molecular configurations with positions, atom types, and charges. A clear acceptance decision.

Pros:

- High significant contribution using equivariant graph neural networks and continuous normalizing flows to obtain invertible equivariant functions.
- The model can lean distributions over molecules considering positions as well as atom types, a clear improvement over previous related normalizing flows, which were focused on positional data.
- The reported molecular generation experiments serve as a clear demonstration for the benefits of their method over other normalizing flows.
- The theory of equivariant flows is heavily based on the derivation from Köhler et al. (2019, 2020) and Rezende et al. (2019), but they contribute a proof for equivalence of the Jacobian of the used subspace and the whole space. 
- Sets a new baseline for molecular structure generation.
- Very well-written paper. The authors motivate this work well, describe all important details of their method, and properly discuss limitations and impact of their work.

Limitations:

- Remains unclear how it performs in comparison to other, nonflow, generative approaches.
- Energies of the generated molecules are not reported.

The above list of pros and few existing limitations make this work highly relevant and worth an oral presentation.
Decision: Accept (Oral)