Title: Physics-informed generative model for drug-like molecule conformers
Venue: NeurIPS 2023
Accepted: no
Keywords: deep learning

graphical models

Probabilistic Models and Methods

Bioinformatics and Systems Biology
Abstract: Diffusion-based methods have been successfully applied to molecule conformer generation using implicit physical modeling. In contrast, conventional, rules-based approaches employ an explicit physical model such as a classical force field parameterization. In order to combine the advantages of both approaches, we present a diffusion-based, physics-informed denoising model (PIDM) for conformer generation that is constructed from molecule subgraph patterns borrowed from classical force fields. The result is a model that is resistant to overfitting and explainable. Using recent advances in denoising score matching, we naturally separate the task of training and generation while providing a smooth transition between deterministic and stochastic generative schemes that adapt to any number of denoising steps. We demonstrate conformer generation quality that outperforms the current state-of-the-art while employing a fraction of parameters.

Abstract

Diffusion-based methods have been successfully applied to molecule conformer generation using implicit physical modeling. In contrast, conventional, rulesbased approaches employ an explicit physical model such as a classical force field parameterization. In order to combine the advantages of both approaches, we present a diffusion-based, physics-informed denoising model (PIDM) for conformer generation that is constructed from molecule subgraph patterns borrowed from classical force fields. The result is a model that is resistant to overfitting and explainable. Using recent advances in denoising score matching, we naturally separate the task of training and generation while providing a smooth transition between deterministic and stochastic generative schemes that adapt to any number of denoising steps. We demonstrate conformer generation quality that outperforms the current state-of-the-art while employing a fraction of parameters. 1

1 Introduction

Conformer generation is the process of identifying a valid and useful set of atomic coordinates for a given molecule. Because it plays a crucial role in structure-based drug-discovery [1], over four decades of effort has been invested in conventional rules-based approaches [2, 3, 4, 5, 6, 7, 8, 9]. Recent advances in generative techniques in deep learning, particularly in diffusion-based models of image generation [10, 11, 12, 13] and point-cloud generation [14, 15], suggest that generative techniques could lead to a renaissance in this field.

We describe in this work is a method of conformer generation using a physics-informed, denoising model (PIDM). By taking advantage of established methods employed in classical force fields, we have constructed a diffusion-based model that is explainable, transferable, and robust. Building upon recent theoretical advancements [16], we employ a flexible method of generation that smoothly adapts to either deterministic or stochastic modes and naturally scales to any number of denoising steps. This is the first time that a physics-informed approach has been applied in a denoising model of this type, the first that is explainable, and the first to feature deterministic generation. The result outperforms the current state-of-the-art while using ten times fewer steps. In addition, we demonstrate a proof-of-concept guided technique that permits targeted generation.

To build a useful tool, we need to generate molecule conformers that are physically meaningful. The naive approach is to directly train a generic, implicit model of physical viability. A drawback is that the number of possible drug-like compounds is too large (by some estimates, as large as 10 33 [17]) to cover in a dataset. Another issue is that the number of viable conformations for each drug-like molecule is intractable in many cases [7]. Therefore, we are forced to limit ourselves to a suitable approach that can readily transfer to molecules and conformations outside a training set.

The first step is to define what constitutes a viable conformer. We use physics as a guide. To appreciate 35 what constitutes a local minima in molecular energy, consider classic force field parameterizations, 36 an established methodology [18]. Force fields are commonly formulated as the sum of 'bonded' 37 and 'nonbonded' contributions [19, 20, 21]. The former include contributions associated with 38 intramolecular bonds and the latter captures longer-distance interactions. The bonded contributions 39 in a classical force field are conventionally divided into four terms: bonds, bends, proper torsions and 40 improper torsions [19, 20, 21]. Each term is identified with a subgraph of a specific topology and one 41 characteristic scalar parameter (Fig 1). These terms will become important in the construction of our 42 model. 43

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In the context of classical force fields, the set of viable molecule conformers are commonly defined 44 in terms of fixed bond lengths, bond angles, and improper torsions. The constraint on proper torsions 45 is cyclic in the angle ϕ such that energy is commonly parameterized as a function of nϕ -ϕ 0 , where 46 n is an integer and ϕ 0 is a reference angle. The freedom to select one of n torsion angles is one way 47 a molecule can exhibit multiple conformations. We will refer to such freedom as torsional space . 48

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Nonbonded contributions to energies depend on external conditions, such as whether the molecule is solvated or bound to a protein [22]. As such, in many applications, nonbonded energies are ignored or attenuated during the process of conformer generation, to avoid biases [23]. We employ this strategy in this work. It can be considered adequate for tools that perform their own search in torsional space, such as flexible ligand docking [24, 25, 26, 27, 28].

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In addition to locating energy minima, a useful conformer generator must respect stable stereochemistry, specifically chirality [29] and cis-trans isomerism [30].

1.1 Related Works

Conventional approaches use a variety of schemes [4, 5, 6, 7, 8, 9, 24]. Balloon [5] is a conformer generator based on a multiobjective genetic algorithm. ETKDGv3 [9] is a knowledge-based generator provided by RDKit [31] based on distance geometry. The OMEGA toolkit [7, 32] employs a fragment library combined with rules-based sampling. Although widely adopted, conventional methods rely on hand-tuned algorithms and are typically limited in accuracy due to an overdependence on classical force fields parameterization.

Several strategies have been employed for learned models, such as energy gradients [33, 34, 35], Gibbs sampling [36], and conditional variational encoders [37, 38]. The drawback of these approaches is that the energy of disordered molecule systems is difficult to characterize directly due to singularities and large energy barriers. GeoMol [39] learns local structure and applies incremental construction. Since incremental construction is poorly suited to cycles, it fails to reproduce all but the simplest ring systems. GeoDiff [40] is a state-of-the-art stochastic diffusion model. It follows conventions most closely related to 'denoising diffusion probabilistic models' (DDPM) [10], employs 793,858 weights and uses 5,000 steps for generation. GeoDiff attempts to model nonbonded distances which requires it to sample torsional space during training. This is not only undesirable (since torsional space is physically ambiguous) but is also likely the reason for a high level of computational complexity.

Others have proposed methods that generate novel molecules in 3D space [41, 42, 43, 44, 45, 46], 73

2 Model Design 75

Our goal is to construct a model that can generate acceptable conformers for any drug-like molecule 76 when provided with just the atom composition, connectivity, and stereochemistry. Recent work [16] 77 has demonstrated that the design of diffusion-based models for images can be generalized around 78 the concept of denoising score matching [47]. We apply this approach to conformer generation by 79 representing our model as a denoising function D that provides an estimate of the true coordinates x 80 of a molecule when provided with coordinates that have been smeared by a centered, uncorrelated 81

Gaussian of width σ 82

where a is a suitable embedding that represents the composition of the molecule ( i.e. its atom types 83 and connectivity). 84

The overall structure of the model is shown in Fig 2 and consists of two major components: a graph 85 transformer network to build a useful atom embedding and a series of bonded subcomponents whose 86 outputs are summed together for coordinate prediction. 87

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The purpose of the graph transformer network is to place the atoms of each molecule into a suitably 88 descriptive embedding space that can be employed by the bonded components. It starts with a 89 embedding in which atoms are distinguished by their element, formal charge, and hybridization. The 90 latter is taken from the algorithm built into the RDKit cheminformatics library [31]. All hydrogens 91 are treated as explicit. Atoms that are associated with explicit chirality or cis-trans isomerisms are 92 flagged by the addition of a global vector reserved for this purpose. 93

The initial atom embedding is refined by multiple layers of a graph transformer network, based on 94 GATv2 [48], and configured to use bonds as graph edges. No edge labeling (such as bond order) is 95 employed, since connectivity along with atom identity is sufficient to describe relevant chemistry [49]. 96 To preserve a form of atom self-identity, rather than use self edges (a poor physical analog), the input 97 to the graph attention network is concatenated to the output. 98

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Each of the bonded components have a similar structure in which a multilayer perceptron (MLP) is used to calculate a correction to atom positions as a displacement along a vector. The details, outlined in the supplemental materials, are summarized here. For the bond component, the vector is the difference δ ij of the two atom positions. The input to the MLP is the concatenation after a suitable normalization of {| δ ij | , σ, a i , a j } , where a are the atom embeddings.

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For the bend component, the vector δ ik is between the two outer atoms. The MLP is fed {| δ ik | , σ, a i , a j , a k , c ijk } , where c ijk is a embedding capturing the size of the rings (if any) to which the bend belongs. The latter is important because the GATv2 graph network, like all message passing networks, is incapable of detecting cycles [50].

For the proper torsion component, the vector δ il is between the two outer atoms. The MLP is fed 108 {| δ il | , σ, a i , a j , a k , a l , sin ϕ, cos ϕ } . The torsional angle ϕ is needed to account for torsional space. 109

The chirality component is constructed out of the improper torsions associated with each chiral 110 atom. The vector is the normal of the plane defined by three of the four atoms. The MLP is fed 111 { d ⊥ , d ∥ , σ, a i , a j , a k , a l } , where d ⊥ ( d ∥ ) is the distance of the fourth atom out of (along) the plane. 112 The cis-trans component is constructed out of the proper torsions associated with each constrained 113 bond. The vector is the difference δ ijkl between the average positions of the outer and inner atoms. 114 The MLP is fed {| δ ijkl | , χ ijkl , σ, a i , a j , a k , a l } , where χ ijkl is the requested cis-trans state. 115

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For the models reported here, an atom embedding of dimension 50 is used throughout. Four graph transformer layers are employed. The MLP for each component uses two hidden layers. The result is a model with a total of 135,080 weights, with 63,480 reserved for the molecule graph and 71,240 in the geometry components. Experiments in increasing the atom embedding dimension or adding additional transformer layers produced only marginal improvement in loss.

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3 Datasets

We are interested in high-quality conformers of drug-like molecules. Two synthetic, publicly available datasets fit this role: QMugs [51] and GEOM-drugs [52]. Each contain several hundred thousand drug-like molecules with conformers optimized (in vacuum) using the GFN2-xTB semiempirical quantum mechanical method [53, 54]. We discard about 2% of the GEOM-drugs molecules due to conformer inconsistency at the graph level. Otherwise, we accept all conformers in both data sets. Both are randomly divided into their own training (80%), validation (10%), and test (10%) subsets.

To measure molecule similarity, we use the Tanimoto measure applied to an ECFP6 fingerprint [55] folded to 1024 bits. At a threshold of 0.9 (0.8), we find 5.6% (6.4%) of the compounds in QMugs overlap with those in GEOM-drugs. Although the two datasets contain mostly different molecules, the underlying physics will be the same. To test dataset independence, we have chosen to train two versions of our model on the two corresponding training subsets, which we will label PIDM[Qmugs] and PIDM[GEOM-drugs]. Both models and others will be compared to a single benchmark dataset, whose preparation is described below.

For the benchmark dataset, we started from the QMugs test subset. To ensure independence and guard against data leakage, we filter each molecule against the contents of the QMugs training subset, the entire GEOM-drugs dataset, and internally using a Tanimoto threshold of 0.7. The annotated chirality and cis-trans isomerism are then validated against the public PubChem database [56]. We also queried PubChem for a copy of the first ten of their generated conformers [23] for comparison. Molecules that could not be validated or did not have a PubChem conformer were discarded. The final result is 15,763 fully annotated, independent molecules reserved for benchmarks.

4 Training

In this work, we follow the modular scheme for diffusion-based models as proposed by Karras et al. [16] in which training and generation are separate tasks that need not share the same noising schedule. For the purposes of training, we chose to evenly sample from the set { σ 1 . . . σ N } :

The total loss L is calculated as the weighted sum of the contribution from each sample σ i 146

Standard parameter values are N = 100 , σ max = 8 Å, σ min = 10 -5 Å, ϵ = 10 -5 Å, and ρ = 6 .

PIDM[Qmugs] is trained using a fixed schedule of 100 epochs, taking approximately 50 hours on a single RTX 3090 (Fig. 3a). PIDM[GEOM-drugs] is trained using a fixed schedule of 25 epochs, taking approximately 170 hours (Fig. 3b).

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Building the model with explicit components has the advantage of explainability. Once provided with 152 an example molecule, each of the bonded compounds can be probed for specific atoms, a process that 153 was invaluable during development. An example is shown in Fig 4. More examples are included in 154 the supplemental materials. 155

5 Generation

We adopt a score-based, probability-flow framework [13] in order to generate conformers from our denoising model. As is typical in this approach, we consider a multidimensional Wiener process applied to molecule coordinates x over a time interval t ∈ [0 , 1] :

where y ( t ) are the resulting random coordinates and σ ( t ) is a width schedule we are free to choose to 160 suit our task, with the only requirement that lim t → 0 σ ( t ) = 0 . For generation, we start by sampling 161 from a random Gaussian distribution N (0 , σ (1) 2 I ) as an approximation for y (1) and solve for the 162 corresponding reverse process (denoising) to obtain y (0) as a candidate solution for x . 163

To construct a solution for the reverse process, we identify the marginal distribution p ( y ; σ ) as 164

where the t dependence is implicit and p ( x ) represents the marginal distribution of the training data. 165 We can use p ( y ; σ ) to express the time dependence of y as a probability-flow ODE [16]: 166

where ∇ y log p ( y ; σ ) is the score function and ˙ σ is the time derivative. In a score-based framework, 167 there is a direct relationship between the score function and our denoising model D [16, 47]: 168

This important result connects our denoising model to the conformer generation process.

In our implementation, we have selected a linear function σ ( t ) = αt , where α is a scale parameter in units of Å. Applying this selection to Eq. 7 and 8 results in a simple form for the probability-flow ODE:

Our conformer generation process is the numerical solution to this equation, calculated in steps of t in reverse, and using as initial conditions y (1) ∼ N (0 , α 2 I ) .

Inspired by work elsewhere [16], we solve Eq. 9 using Heun's 2 nd -order method, augmented by a form of backtracking (Algorithm 1). The backtracking provides an option to add additional noise to the generation process. We begin by dividing the interval [0 , 1] into a fixed partition { t i } over which we iterate in order to calculate a set of intermediate solutions { y i } . Instead of relying on solving on the partition { t i } , we substitute modified values for the upper bound t i of each subinterval:

where β ≥ 1 and λ ≥ 0 are fixed parameters. This has the effect of introducing Gaussian noise at each step of the solution. For λ = 1 , the amount of added noise compensates for the change in subinterval size.

For reasons of convenience, we remove an overall center-of-mass during each generation step. The correction is small and quality of output is not affected.

If we generate using λ = 0 , no noise is added during the intermediate steps, resulting in deterministic generation. Combined with β > 0 , the algorithm is equivalent to pretending that each intermediate value y i belongs to a solution sampled from a larger value of σ . This has the effect of overcorrecting, which improves accuracy in our case.

Alternatively, if we generate using λ > 0 and β > 0 , we inject noise during each step for stochastic generation. Both stochastic and deterministic approaches have been used for image generation, with impressive results [10, 11, 12, 13, 16, 57, 58, 59].

To apply our algorithm, we use the partition { t 1 . . . t N } of a given size N and final step size t ϵ :

The quality of generated output is reasonably stable for a large range of parameter values. The results 193 reported here use t ϵ = 0 . 0006 , α = 2 . 5 Å, and β = 5 . Quality improves marginally if the solution is 194

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calculated using more steps at a proportional cost in processing time. To quantify this trade off, we report on results for N = 100 , 200, and 500. We also report results for both deterministic ( λ = 0 ) and stochastic ( λ = 1 ) generation.

Shown in Fig 5 are random examples of generated conformers, using PIDM[QMugs], deterministic generation, and 500 steps. More examples are available in the supplemental materials.

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6 Experiments

Our objective is to generate molecules with valid bonded geometry. To demonstrate accuracy, ten random conformers were generated by PIDM[QMugs] and PIDM[GEOM-drugs] for each of the molecules in the benchmark set. Each result was compared against the ground truth represented by the corresponding conformers in QMugs. Overall errors in bond length d and bend angle θ were measured using the mean absolute deviation (MAD). Because proper torsions have multiple favored values, the MAD for ϕ was limited to values generated with ± 30 ° of the angle found in the reference conformer. Failures to reproduce the desired chirality or cis-trans isomerism were recorded as a fraction of total occurrence of associated improper or proper torsion.

Results are shown in Table 1. Also shown are results obtained from other conformer generation solutions. In all cases, ten conformers were requested, although some conformer solutions provide less than the requested number under certain circumstances. The conformers provided by PubChem are calculated under the PubChem3D scheme [23] based on the OMEGA toolkit [32]. ETKDGv3 has known deficiencies and is often followed by gradient optimization based on the MMFF94 force field [6, 21]. We used the GeoMol checkpoint (GEOM-drugs) provided by the authors.

We tested the GeoDiff checkpoint trained on GEOM-drugs provided by the authors. This model performs well on d and θ , but struggles with ϕ . GeoDiff has no mechanism for enforcing chirality

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nor cis-trans isomerism, an omission that appears to be an oversight rather than a limitation of the approach.

7 Guided Generation

Our model makes no attempt to predict distances between nonbonded atoms. This suggests that there are degrees of freedom available during generation that are being ignored. Addressing this deficiency could provide a valuable measure of control over the torsional space.

Before experimenting, we require a control. The torsional space sampled in the synthetic QMugs and GEOM-drugs data sets were established by their authors based on explicit yet arbitrary criteria, which makes them uninteresting. Instead, we can refer to experimental data. The authors of the OMEGA toolkit selected two small experimental sets for this purpose [32]: 480 molecules from the Cambridge Structural Database (CSD) and 197 ligands from the PDB. As shown in Table 2, RMSD performance of our model lags that obtained from OMEGA and RDKit+MMFF94.

Consider a modified, probability-flow ODE:

where F ( y ) is introduced to guide generation in a desired fashion. Solving for Eq. 12 in place of Eq. 9 provides a mechanism for guided generation where F ( y ) serves as a form of conditional score [60].

As a simple proof-of-concept, consider F ( y ) = η ∑ ( b 2 + δ 2 ) -5 , summed over all nonbonded atom pairs, where δ is the distance between atoms, b = 0 . 7 Å, and η is an overall magnitude. This term is analogous to a repulsive force similar to what is found in the van der Waals interaction. The result is a modest improvement in RMSD statistics on the CSD and PDB experimental data sets, as shown in Table 2. Statistics on bond parameters (Table 1) are largely unaffected, with the notable exception of an increase in chirality failure rates.

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8 Discussion

The PIDM[QMugs] and PIDM[GEOM-drugs] models, despite being trained on datasets with little overlap, perform similarly on all benchmarks. Probes indicate that both models have learned similar solutions. We contend that this level of robustness could only have been achieved by capturing the important, underlying physics. Unlike conventional approaches to conformer generation, which either rely on curated template libraries or manually-tabulated force field parameterizations, the physics in our model is entirely learned.

PIDM is explainable. The advantage this provides cannot be overstated. The ability to probe the internal structure during development permitted a level of experimentation that would not have been possible in a black-box implementation.

For generation, we numerically solve for the probability-flow ODE, using a form of oversampling. By separating the training and generation tasks, we were free to explore multiple approaches without retraining. Using deterministic generation, we were able to produce conformers of reasonable quality in as little as 100 steps. This is in stark contrast with GeoDiff [40], the current state-of-the-art diffusion model, which employs stochastic generation in 5,000 steps.

For reproducing bonded parameters, PIDM with 500 steps has comparable performance on average to conventional methods (such as OMEGA and ETKDGv3). It outperforms GeoDiff with 1/6 the number of weights.

8.1 Limitations

Conformer generation for molecules with chemical groups or atom types outside the training set may perform poorly or fail. Molecules with certain challenging topologies, such as a central ring with several large branches, may perform poorly (an example is given in the supplemental materials). Conformer quality is expected to degrade as molecules grow in size beyond ∼ 200 heavy atoms.

The atom embedding used in our model was generated using GATv2 [48]. We suspect that using a type of graph network that can capture the same quality of atom-type information while also recognizing cycles would improve performance.

9 Conclusion

Presented is PIDM, a diffusion-based model inspired by the bonded components of classical force 266 fields. Parameters were trained on high-quality conformers from the QMugs and GEOM-drugs 267 data sets. Learning appears robust, transferable, and explainable. Both deterministic and stochastic 268 generation schemes are demonstrated. Average performance on the reproduction of bonded parameters 269 is comparable to conventional conformer generation tools. A simple example of guided generation is 270 successful at improving torsional sampling when compared to experimental data. 271

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes PIDM, a novel generative model for generating 3D molecular conformations from 2D molecular graphs. The proposed method uses an ODE based diffusion model to generate 3D molecular conformations, and designs a denoising network with multiple different modules to capture various of physical information from molecules. The proposed method achieves better performance than two baseline methods, GeoMol and GeoDiff, in experiments.\n\nSTRENGTHS:\n- This work proposes a series of novel strategy to capture geometric information from different geometric inputs (e.g., bonds, bends, torsions) by different modules in a model. The proposed model architecture can be useful for a variety of molecular machine learning tasks.\n- Experimental results show that the proposed method achieves promising performance when compared with two strong baseline methods, GeoMol and GeoDiff, in benchmark datasets.\n\nWEAKNESSES:\nMajor:\n- A major weakness of this paper lies in that many necessary details of the proposed method is not presented or not sufficiently described as detailed below.  \n(1) The proper torsions and improper torsions introduced in line 40-41 are not formally defined and it is not easy to discriminate them by Figure 1. Also, it is not clear why the model has a module for proper torsions but no module for improper torsions.  \n(2) It is not easy to understand why \"The constraint on proper torsions is cyclic in the angle $\\phi$ such that energy is commonly parameterized as a function of $n\\phi-\\phi_0$\" (line 46). Does it mean that proper torsions are periodic and $\\phi$ is the periodicity? How this constraint is incorporated in the designed model?   \n(3) The details of several modules are not described in Section 2. The details of the computation process in graph attention module is not described. The cis-trans module in Figure 2 is not introduced. Also, it is not clear what is the output (\"solution\" in Figure 2) of the model, is it the atom embedding, or the denoised atom coordinate? How the outputs are computed if they are not atom embeddings?  \n- For experiments, it would make results stronger if authors can do comprehensive ablation studies about the proposed novel modules in the model as they are the major novelty contributions. Also, it is recommended to compare with an important baseline method, Torsional Diffusion [1].\n\nMinor:\n- To make a better organization, it would be better to move Section 3 Datasets to the place just before Section 6 Experiments as they are more closely related.\n- It is hard to understand what Figure 4 tries to show. What do the y-axis values mean? And how these curves are related to explainability? Authors may make more clarification, and are recommended to move these results to experiment part to maintain a better organization.\n\n[1] Torsional Diffusion for Molecular Conformer Generation. NeurIPS 2022.\n\nQUESTIONS:\nNo additional questions.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2023-07-04"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper presents a diffusion model to generate conformers of drug-like molecules. The score model architecture is novel.\n\nSTRENGTHS:\nThe authors construct a diffusion model for conformer generation whose score model architecture is inspired by the structure of classical force fields. This is an interesting approach and quite different from the SE(3) or E(3) equivariant graph neural nets that are popular for this kind of problem.\n\nWEAKNESSES:\nI found parts of the paper to be quite unclear.\n\nLine 46: I don’t understand this $n\\phi - \\phi_0$ expression or ‘freedom to select one of $n$ torsion angles’. Is there a discrete set of admissible torsion angles? Sorry, I’m ignorant about molecular geometry – but so will be many of your readers at NeurIPS.\n\nLine 71 ‘attempts to model nonbonded distances which requires it to sample torsional space during training… torsional space is physically ambiguous’: I don’t understand these sentences.\n\nFigure 2: what shape is the output from each of the pink blocks? Is it (number of atoms) * 3? What is the regression target for the summed ‘solution’? In some works on molecule generation or conformation prediction, the regression target is the noise that was added to the atom positions, and in other works the regression target is the ‘clean’ atom positions from the training data, so this needs to be clarified.\n\nLine 125: what is ‘conformer inconsistency at the graph level’? \n\nSection 4 Training: if you want to experiment with different samplers after training then I think that during training you should sample values of $\\sigma$ from a continuous range, rather than picking from N discrete values. If you sample by stepping through values of $\\sigma$ not seen during training, you will be presenting the score model with inputs it never saw during training, and I expect the performance will be suboptimal.\n\nFigure 4: please explain what the x and y axes are here. In general, I did not understand the ‘explainability’ aspect of the work.\n\nLine 216: I think that the inability of GeoDiff to discriminate between a molecule and its mirror image is a fundamental issue with the GFN architecture.\n\nTable 1 caption says 'best values in each category are highlighted' but I cannot see the highlight (perhaps a printing problem).\n\nThe guided generation task in section 7 seems arbitrary. I do not understand equation (12) because in the right-hand-side numerator we have a vector $y$ and then subtract $F(y)$ which appears to be a scalar.\n\nQUESTIONS:\nLine 95 ‘uses bonds as graph edges’:  why not allow some message-passing between non-bonded atoms?\n\nLine 127: is any clustering used to split the data, or can similar molecules appear in both training and test data?\n\nCould you please elaborate on the explainability of the model? For example, show examples of predictions and their explanations. Perhaps this is meant to be shown in Figure 4 but I did not understand it.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2023-07-04"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nA diffusion-based conformation generation method called PIDM is proposed for molecules. It combines several geometries including bond lengths, bend angles, proper torsions, chirality and cis-trans of the noisy conformer as the input, and output the scores of the probability to iteratively generate the conformations. Experiments shows the robustness of the model, while is not convincing enough to show the performance of PIDM.\n\nSTRENGTHS:\n- The proposed model is simple yet effective, with a smaller NFE used compared to GeoDiff.\n- Many version of the proposed DIPM has been test in the experiments.\n\nWEAKNESSES:\nSeveral problems exist, so that I think it is not a mature enough article to be published.\n\n1. Confusing presentation and limited novelty. \n\n- First, it is a physics-informed method, but I cannot find supports that there are some physics knowledge as priori knowledge that works in the model. The five geometries are very commonly used that conformation generation methods focus on, such as torsion angle in TorsionalDiff[1] and distance in CGCF[2]. It is not a novel idea based on physics rule. In the guided generation, some of the physics-based or energy-liked terms is used to modified the generating process, but it is not the main contribution of the paper, but a simple experimental attempt. \n\n- Second, the structure of the article is not well-organized. The description of the proposed method is very short, and not completely explained. More details with formulas should be added. The dimension of embedding sizes and other experimental details should be included in the experiment parts. Description of datasets and preprocessing should also placed in the experiment sections. In Sec. 5, most of the details has been given in [3], and the generation process is just an implementation of it, so it can be presented in a brief way, since it is not the main contributions. However, it takes up an entire page, almost the same as the designed method which is your main contributions.\n- Third, several parts are not well explained. For example, in Figure 2, what is the red arrow means, and what is the black means. Figure 3 is the loss in the training procedure on training a validation set, but what are you try to tell the readers? If you want to show the robustness of the model, some of evidence about other models are not robust should be compared, since most training/validation loss plots seem to be the same like Figure 3. There are also several similar examples.\n\n2. Symmetries are not considered. As a diffusion models, most methods will consider the SO(3) equivariance or E(3) equivariance of the denoisers, leading the probability model to satisfy $p(x) = p(\\Pi x)$ in which $\\Pi$ is a matrix representation of the certain group. However, in PIDM, the output is scores of 3D-positions each atoms, but the input is the invariant geometries like bond lengths and angles, so if the noisy positions are rotated, the geometries will be unchanged, and the scores will also not be rotated. The equivariance is not ensured. (I am not very certain about it, because the detailed of model is not fully described in Sec.2, and the input and output of the model is mostly based on my guesses.) \n\n3.  Incomplete experiments.\n- The experimental protocols and compared baselines are not convincing. As the new SOTA method, TorsionalDiff shows better experimental performance compared to GeoMol. Both of these two methods generated a conformer based on a prior conformer generated by RDKit. Therefore, at least TorsionalDiff should be included as a baseline, and also, the experimental protocols such as metrics like Recall Coverage/AMR and Precision Coverage/AMR. The GeoDiff is only trained on a very small part of Drugs, but the checkpoint is directly employed for comparison.  Is it reasonable? Or it should be trained on the same training set and test on validation set? For GeoMol as another deep-learning-based models, should it be re-trained and tested with the same protocols to should the superiority of the PIDM?\n\n- The comparison on geometries of generated molecules and ground-truth molecules is interesting, but some detailed comparison should be added. For example, the distribution of C-C, C=C bond distance of baselines, PIDM, and ground truth, or other bend angles, torsion angles, etc., and the JS-diversity between the distributions. Only the MAD cannot fully demonstrate the superiority of the performance. \n\n- In the abstract, it says that the model is resistant to overfitting and explainable. In which part of the experiments gives demonstration of these two advantages of the models. Can PIDM trained on Drugs generalize well on QMugs? If it can, the two datasets consist of molecules of similar sizes (25 ~ 30 atoms),  how about smaller molecules in QM9 or larger ones in ligands in PDBBind? How the model shows explainability? \n\n- The sampling method used is in [3], what is the performance gain it brings compared to the original score-matching sampling methods? If there is no improvements according to empirical comparison, why it is employed? As I know, TorsionalDiff also use a very small NFE during sampling, so in evaluating effectiveness, does PIDM work better?\n\n\n[1] Bowen Jing, et al, Torsional Diffusion for Molecular Conformer Generation, https://arxiv.org/pdf/2206.01729.pdf\n\n[2] Chence Shi, et al. Learning Gradient Fields for Molecular Conformation Generation, https://arxiv.org/pdf/2105.03902v1)%3C%22\n\n[3] Tero Karras, et al. Elucidating the Design Space of Diffusion-Based Generative Models, https://arxiv.org/pdf/2206.00364.pdf\n\nQUESTIONS:\nThe questions are given in the weakness part. Please refer to the points that I am doubtful about.\n\nLIMITATIONS:\nN. A.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-06"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a physics-informed generative framework targeted at the task of molecular conformation generation. The method is motivated by the formulation of classical force fields and such an idea is reflected via bond, bend, and proper torsion and properly injected into the model design. The experiments are conducted on GEOM-Drugs and QMugs datasets in terms of molecule conformation generation.\n\nSTRENGTHS:\n1. The paper is well-motivated via the lens of classical force fields and the method contains reasonable integration of the idea.\n\n2. The method is easy to follow with necessary details presented to help understand the entire pipeline of the generation framework.\n\nWEAKNESSES:\n1. The experimental evaluations lack the necessary details and discussions, which brings concerns about the credibility of the experimental comparison with the baselines (see Q1 and Q3).\n\n2. Important baselines are missing (see Q2).\n\nMinor: Some parts of the presentation of the paper are confusing and may require further checks and polishment, e.g., line 246. In figure 5, is it possible to include some conformations generated by the baselines to offer the readers a clearer qualitative comparison?\n\nQUESTIONS:\n1. In this paper, the authors seem to simply use the open-sourced checkpoints of the baselines like GeoMol and GeoDiff to report the testing results. However, it is uncertain whether the entire training protocol is fair compared with the original setups in these baseline papers. More justifications should be addressed on this point to ensure that the experiments offer a fair comparison.\n\n2. Important baselines, e.g., Torsional Diffusion [1], are missing and should be discussed and compared since they share a similar/relevant idea of leveraging physical priors of bond/bend/torsional angles.\n\n3. Why do the evaluation protocol and metrics seem so different from previous works like GeoMol and GeoDiff? Is it possible to conduct experiments following the widely-adopted setup in order to make a convincing comparison?\n\n\n[1] Jing, Bowen, et al. \"Torsional diffusion for molecular conformer generation.\" Advances in Neural Information Processing Systems 2022.\n\nLIMITATIONS:\nThe authors have satisfactorily discussed the limitations.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2023-07-07"}