We are grateful for the reviewer's careful evaluation and constructive suggestions, which have helped us improve the manuscript. Below, we respond to each comment in detail. We hope our clarifications and corresponding revisions have resolved the key issues, and we would appreciate it if this could be reflected in the final evaluation.

The main weakness of this work is its limited novelty. Transferring a model with minimal adjustments from one modality to another does not, in my humble opinion, clear the bar for NeurIPS. Though I reckon that this point is subjective, and acknowledge if other reviewers disagree.

We thank the reviewer for acknowledging that the evaluation of novelty can be subjective, and we would like to respectfully offer a different perspective on the novelty and significance of our work. While our approach builds upon an architecture originally developed for the perceptual domain of computer vision, the successful adaptation to the domain of physically accurate molecular conformer generation required non-obvious and technically meaningful modifications, far from a straightforward transfer. Specifically, we solve the following, domain-specific challenges:

• We introduce a novel GNN-based conditioning mechanism to incorporate molecular graph information, which we show is crucial for conformer generation (Appendix H). Our approach departs from the global or text-based conditioning typical of image-based DiTs by leveraging both node-wise and pair-wise conditioning strategies (applied to atoms, bonds, or all atom pairs). We find and highlight significant differences in effectiveness among these strategies in our ablation experiments (Appendix Table A8).
• As part of this framework, we propose using geodesic graph distances as conditioning information. We are not aware of any other approach that uses geodesics (shortest paths) on the graph to condition the self-attention mechanism operating on the molecular geometry in 3D space. We have added a dedicated ablation (Table R1) of this component, validating that it is critical to the competitive performance of DiTMC.
• We investigate the role of incorporating physical symmetries into the model. We discuss the trade-offs between fidelity and computational cost when dealing with the 3D nature of molecular data in accordance with geometric principles.

Our ablation studies (Appendix E-H, K) and Table R1 demonstrate that removing any of the proposed architectural innovations leads to a substantial performance drop. Collectively, our contributions provide a comprehensive toolkit for adapting DiTs to the molecular domain, with a particular focus on conformer generation, including substantive technical innovations that extend beyond naive architectural transfer. These novelties enable DiTMC to improve upon all other state-of-the-art methods in terms of precision metrics, size extrapolation, and precision-speed Pareto front. We think the strong empirical evidence should not be overlooked when judging the novelty of our model.

Table R1. Ablating the effects of our proposed conditioning strategy via graph geodesics on GEOM-DRUGS. Relative improvement indicates how much the regular model benefits from using graph geodesics.

The experiment sections are inconsistent in that while rPE in all experiments within the main body and the appendix is the best performing method, it does not occur in most tables.

Why is rPE frequently omitted?

We thank the reviewer for pointing out this inconsistency in the presentation of our results. As stated in the original manuscript, we initially focused on the models using aPE and PE(3) on GEOM-DRUGS, as they represent the extreme cases of not including any, and including all Euclidean symmetries in the architecture design. We agree that this focus might be misleading and added a study on the performance of rPE models on GEOM-DRUGS to address the reviewer’s concern.

We have now included DiTMC+rPE-B on GEOM-DRUGS in all relevant tables (see Tables R2, R3 and R4 based on Tables A10, A11 and A13 in the original manuscript). The training for DiTMC+rPE-L on GEOM-DRUGS is still in progress. We will be happy to share the results during the discussion phase, and we will include all results in the final version of the paper.

Table R2: Results on GEOM-DRUGS for different DiTMC variants. -R indicates Recall, -P indicates Precision.

Table R3: Median absolute error of ensemble properties between generated and reference conformers for different DiTMC variants on GEOM-DRUGS.

Table R4: Out-of-distribution generalization results on GEOM-XL for different DiTMC variants trained on GEOM-DRUGS. -R indicates Recall, -P indicates Precision.

The empirical gains compared to previous works are present but limited.

While the absolute numerical improvements may appear modest in some cases, they are consistent across a wide range of datasets and evaluation metrics (see Tables 1-4 in the original manuscript). Notably, no other method in our comparison achieves this level of consistency (across precision, out-of-distribution performance and accuracy of ensemble properties), which we believe is a key strength of our approach. In real-world applications, such robustness and generalization are often even more valuable than isolated gains on individual benchmarks. We compare against strong, well-established baselines that are already highly optimized. In such a setting, even moderate improvements reflect meaningful technical progress and nontrivial methodological innovation.

Specifically, our DiTMC+aPE-L model shows a relative improvement from 3.3% up to 12.4% in precision metrics compared to existing state-of-the-art methods (see Table 1 in the original manuscript).

In terms of out-of-distribution performance in GEOM-XL we show relative improvements over the current state-of-the-art model MCF-L ranging from 3.9% up to 15.2% (see Table R5 based on Table 4 in the original manuscript).

Following the experiments performed in ET-Flow and MCF, DiTMC outperforms existing methods for a tighter acceptance threshold. To that end, DiTMC yields relative improvements up to 38.4% for a threshold of 0.1Å (see Table R6). This shows that our generated conformers are significantly closer to the ground truth conformers than the ones generated by other methods.

Compared to the current state-of-the-art models ET-Flow and MCF, we find that our DiTMC+aPE-L is the fastest model, requiring 26 ms per generated conformer, whereas MCF-B requires 28 ms and ET-Flow requires 63 ms on the GEOM-DRUGS dataset. For a fair comparison, we compare models with identical numbers of sampling steps (50 steps). Thus, DiTMC+aPE-L is faster and simultaneously outperforms MCF and ET-Flow in terms of all precision metrics, showing that we can shift the speed-precision Pareto front of current approaches.

We hope our systematic improvements over state-of-the-art methods make it clear that our contributions are meaningful and not limited in scope.

Table R5: Out-of-distribution generalization results on GEOM-XL for models trained on GEOM-DRUGS. -R indicates Recall, -P indicates Precision. We report relative improvements of DiTMC+aPE-L to the best-performing model to date as a positive percentage.

Table R6: Comparison of coverage (COV) metrics for DiTMC+aPE-B to ET-Flow-SS and MCF-L with a RMSD threshold of 0.10Å on GEOM-DRUGS. We report relative improvements of DiTMC+aPE-L to the best-performing model to date as a positive percentage.

The related work section is rudimentary and misses the field of Boltzmann generators.

We appreciate the reviewer’s suggestion and will expand the related work section to better contextualize our work. In short, our approach differs in two key ways from Boltzmann Generators: it explicitly conditions on molecular graph structure to enable transferability, an emerging challenge for BGs [1-3], and employs uniform weighting of conformers to focus on accurate 3D structure prediction over the prediction of thermodynamic ensembles.

[1] Swanson, K., et al., (2023). Von Mises mixture distributions for molecular conformation generation. ICML.

[2] Klein, L., et al., (2023). Timewarp: Transferable acceleration of molecular dynamics by learning time-coarsened dynamics. NeurIPS 37.

[3] Klein, L., & Noé, F. (2024). Transferable Boltzmann generators. NeurIPS 37.

We thank the reviewer for reading and reviewing our submitted manuscript and the overall positive assessment of our work. In the following we address questions and comments of the reviewer in a point-by-point manner.

1/ Computational Cost of Equivariance: While the analysis of the cost-fidelity trade-off is a strength, the high computational cost of the fully equivariant model is a practical weakness. The paper reports that the PE(3) model is approximately 3-3.5x slower than its non-equivariant counterparts, even with a smaller model size. The authors give a dicussion about this in the manuscript, and it sounds reasonable.

As correctly pointed out by the reviewer, equivariant models introduce additional computational cost which can make “small” models computationally costly already. For this reason, reducing the computational cost of equivariant models is an ongoing topic of active research, which can be broadly categorized into two directions: The first class of approaches reduces computational cost by new architectural designs [1, 2] whereas the second class “sparsifies” the cost-dominating SO(3)-convolutions [3, 4]. We hope that our results motivate the adaptation of such approaches in the setting of 3D molecular conformer generation and we will add a short discussion about this within the “Discussion & Limitations” section of our manuscript.

[1] Cen, Jiacheng, et al. "Are high-degree representations really unnecessary in equivariant graph neural networks?." Advances in Neural Information Processing Systems 37 (2024): 26238-26266.

[2] Frank, J. Thorben, et al. "A Euclidean transformer for fast and stable machine learned force fields." Nature Communications 15.1 (2024): 6539.

[3] Luo, Shengjie, Tianlang Chen, and Aditi S. Krishnapriyan. "Enabling efficient equivariant operations in the fourier basis via gaunt tensor products." arXiv preprint arXiv:2401.10216 (2024).

[4] Maennel, Hartmut, Oliver T. Unke, and Klaus-Robert Müller. "Complete and efficient covariants for three-dimensional point configurations with application to learning molecular quantum properties." The Journal of Physical Chemistry Letters 15.51 (2024): 12513-12519.

The paper uses two variants of model size, "Base" and "Large", demonstrating a clear trade-off: the non-equivariant aPE model scales efficiently in terms of computation and achieves state-of-the-art precision, while the fully-equivariant PE(3) model offers higher fidelity at a significant computational cost. Which direction is more promising when scaling this framework up to much larger and more complex systems? Please comment.

In general, our equivariant models require significantly more compute for the same number of parameters, due to the presence of equivariant representations and SO(3)-convolutions. Under limited hardware resources, scaling the PE(3) model quickly becomes a bottleneck; for example, we observe OOM on a 40GB GPU with our PE(3)-L model for a batch size of 128 on GEOM-DRUGS. On the other hand, the equivariant model converges faster during training, as it does not require learning the equivariance of the target vector field through data augmentation during training. Nevertheless, under the same compute budget, aPE outperforms PE(3) for most metrics on the larger GEOM-DRUGS benchmark. During inference, the aPE-L model is a factor of 3 faster than the PE(3)-L, but the PE(3)-model produces higher fidelity structures (Fig. 2).

Scaling this framework to larger and more complex systems requires significantly larger and more diverse training datasets, as well as increasing the number of model parameters. The computational cost per additional parameter grows much faster in the PE(3) model than in the aPE model, such that we expect the aPE model to be more scalable in the limit of large dataset sizes. Our findings on GEOM-DRUGS already indicate this, since we find that the aPE model outperforms the PE(3) model in most metrics when trained with the same compute budget.

During inference, the larger the systems, the faster the aPE model becomes compared to the PE(3) model, due to the substantially smaller pre-factor in the computational complexity. Thus, the benefit of using aPE compared to PE(3) in terms of inference speed grows in system size, and we consider this to be the more promising approach for large-scale training and inference. An exception might be applications, for which only very little training data is available (e.g., data can only be obtained from experimental measurements) and high fidelity is more important than computational speed (e.g., one requires only a few generated structures, but they must be as accurate as possible).

We thank the reviewer for their thoughtful comments. We have carefully addressed all the points raised, and hope that the revisions resolve the primary concerns. We hope that these improvements will be viewed positively and assist in the reviewers’ final evaluation.

Incremental novelty. The core idea—plugging flow-matching/diffusion into a transformer with graph conditioning—extends recent DiT/Flow-Matching work.

Incremental Conceptual Advance. The work mainly repackages existing diffusion/flow-matching ideas within a transformer framework. While the engineering is solid, it introduces no fundamentally new generative principle, limiting its conceptual impact.

We respectfully disagree with the assessment that the conceptual advance of our work is incremental. While we build upon established foundations, namely developments from the perceptual domain of computer vision, a successful adaptation to the domain of physically accurate molecular conformer generation required non-obvious and technically meaningful modifications. We believe our work introduces domain-specific conceptual advances in the following ways:

• We introduce a novel GNN-based conditioning mechanism to incorporate molecular graph information, which we show is crucial for conformer generation (Appendix H). Our approach departs from the global or text-based conditioning typical of image-based DiTs by leveraging both node-wise and pair-wise conditioning strategies (applied to atoms, bonds, or all atom pairs). We find and highlight significant differences in effectiveness among these strategies in our ablation experiments (Appendix Table A8).
• As part of this framework, we propose using geodesic graph distances as conditioning information. We are not aware of any other approach that uses geodesics (shortest paths) on the graph to condition the self-attention mechanism operating on the molecular geometry in 3D space. We have added a dedicated ablation (Table R1) to validate the impact of this component, showing that it is critical to the competitive performance of DiTMC.
• Finally, we investigate the role of incorporating physical symmetries (translations and rotations) into the model. We discuss the trade-offs between fidelity and computational cost when dealing with the 3D nature of molecular data in accordance with geometric principles.

Our ablation studies (Appendix E-H, K) and Table R1 demonstrate that removing any of the proposed modifications to the original DiT architecture leads to a substantial performance drop.

Collectively, our contributions provide a comprehensive toolkit for adapting DiTs to molecular domains, with a particular focus on conformer generation, including substantive technical innovations that extend beyond naive architectural transfer. These novelties ultimately enable DiTMC to improve upon all other state-of-the-art methods in terms of precision metrics, size extrapolation, and precision-speed Pareto front. We think the strong empirical evidence should not be overlooked when judging the novelty of our model. We hope this clarification goes some way toward addressing the reviewer’s concern.

Table R1. Ablating the effects of our proposed conditioning strategy via graph geodesics on the GEOM-DRUGS dataset. Relative improvement indicates how much the regular model benefits from using graph geodesics.

Computational Cost Comparison: While the inference times for DiTMC variants are provided, how do these compare to other state-of-the-art methods (e.g., MCF, ET-Flow) in terms of FLOPs, memory, or wall-clock time? A direct comparison would help assess practical trade-offs.

ET-Flow and MCF do report the sampling time per conformers on the GEOM-DRUGS dataset. We find that our DiTMC+aPE-L is the fastest model, requiring 26 ms per generated conformer, whereas MCF-B needs 28 ms and ET-Flow 63 ms. For a fair comparison, we compare models with identical numbers of sampling steps (50 steps). Thus, DiTMC+aPE-L outperforms MCF and ET-Flow in terms of all precision metrics and is faster at the same time, showing that we are able to shift the speed-precision Pareto front of current approaches.

We agree that this is an important comparison which allows us to highlight the strengths of our proposed framework. Therefore, we will add this experiment to the final version of our manuscript.

Restricted Molecular Scope. All experiments target small- to medium-sized, neutral organic molecules (≤ ~100 atoms). Performance on larger, highly flexible, charged, or metal-containing species—including peptides, macrocycles, and organometallics—remains untested.

We have applied our DiTMC model to the GEOM-DRUGS and to the GEOM-XL dataset, which contain molecules with up to 181 atoms and 232 atoms, respectively. Both datasets actually contain highly flexible, charged molecules as well as molecules with macrocycles and metals [1]. As we are able to show (Table 2 and Table 4 in the original manuscript), DiTMC yields state-of-the-art performance on GEOM-DRUGS and is the best model on GEOM-XL. We hope that this clarification properly addresses the reviewers' concerns.

[1] Axelrod, Simon, and Rafael Gomez-Bombarelli. "GEOM, energy-annotated molecular conformations for property prediction and molecular generation." Scientific Data 9.1 (2022): 185.

Generalization to Large and Complex Molecules: While effective on benchmark datasets, DITMC’s performance on larger, more complex molecules (e.g., proteins or macromolecules) is not fully validated due to dataset constraints. The modular architecture may struggle with the increased structural diversity and conformational flexibility of such systems.

We tested the generalizability of our GEOM-DRUGS-trained DiTMC+aPE-B model on large, flexible molecules: a 512-atom polyalanine peptide and a 502-atom PET polymer. Both yielded accurate conformations, with RMSDs of 2.6 Å and 2.9 Å respectively, against their MMFF94-relaxed structures, confirming the robustness of our model.

Dependence on Training Data Quality: DITMC’s performance relies heavily on the quality and diversity of training datasets (e.g., GEOM-QM9, GEOM-DRUGS). Limited or biased datasets may lead to poor generalization, especially for rare or complex molecular structures.

Heavy Reliance on High-Quality Conformer Labels. Training hinges on well-curated datasets such as GEOM-QM9 and GEOM-DRUGS. In domains where reference conformers are scarce, noisy, or biased, model fidelity and transferability can degrade sharply.

We agree that generative models as a whole strongly rely on the availability of sufficient and also representative training data. To that end, we believe it is a particularly nice property of our presented framework, that it fully supports going from full SO(3) equivariant models to its non-equivariant counterpart. Equivariant models, while being computationally more expensive, have been shown to drastically improve the data efficiency [2], making such models particularly well suited in the low-data regime. We will add a corresponding discussion to the “Discussion & Limitations" section of our manuscript.

[2] Batzner, Simon, et al. "E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials." Nature communications 13.1 (2022): 2453.

Data Quality Sensitivity: The paper demonstrates strong performance on high-quality datasets like GEOM. Could the authors discuss how the model's performance might degrade when trained on lower-quality or noisy conformer data? Are there any built-in robustness mechanisms?

We agree that this is an important point, as the accuracy of the generated conformers is bounded by the accuracy of the training data. This problem has been successfully tackled in other domains of quantum chemistry, by using lower quality data for pre-training and fine-tuning on little but high quality reference data [3]. Adapting such approaches to molecular conformer generation, poses an interesting direction for future research.

[3] Cui, Mengnan et. al. "Multi-fidelity transfer learning for quantum chemical data using a robust density functional tight binding baseline." Machine Learning: Science and Technology 6.1 (2025): 015071.

Scalability to Large Systems: The experiments focus on small to medium-sized molecules. How does DiTMC scale to very large systems (e.g., >400 atoms), such as proteins or polymers? Are there architectural or sampling adjustments needed to maintain efficiency?

To test the computational performance of DiTMC+aPE-B trained on GEOM-DRUGS, we analyse the inference time as a function of the number of atoms on the example of a capped polyalanine peptide with an increasing number of repeating units. Interestingly, we did not need to adjust the number of ODE steps during sampling of larger structures to obtain accurate results, suggesting that the learned velocity field maintains stability and accuracy across different system sizes. Table R2 reports the number of atoms and the time per sample.

Table R2. Time per sample for the capped polyalanine peptide using batch size of 1.

Thank you for your detailed rebuttal. I would consider keeping my score. I'm still interested to see whether this small model can effectively handle de novo molecule generation.

We thank the reviewer for their careful reading and thorough review of our manuscript. Below, we respond in detail to each of the reviewers’ comments.

A key concern lies in the experimental results. While DiTMC-L, as claimed, achieves competitive performance with ~30M parameters (...), there is not a significant performance boost over the ET-Flow - SS baseline (8.3M) on Geom-Drugs. This raises questions about the effectiveness of the proposed approaches.”

2. Could the authors provide a comparison between the base model and ET-Flow - SS baseline (8.3M) over Geom-Drugs?

We agree that all parameter counts should be clearly stated in the main document and will update the manuscript accordingly. However, we would like to clarify, that we achieve better performance than ET-Flow-SS even with our base variants (e.g. DiTMC+aPE-B, 9.5M params) on GEOM-DRUGS (see Table R1 based on Table A10 in the original manuscript) and also in out-of-distribution performance on GEOM-XL (see Table R2 based on Table A13 in the original manuscript), indicating that our improvements are not due to larger model size. In fact, we observe an improvement of DiTMC+aPE-B over ET-Flow-SS for every single metric we investigate. Our relative improvements range up to 4.3% on GEOM-DRUGS and up to 17.1% on GEOM-XL.

Furthermore our base models improve upon ET-Flow-SS in terms of sampling speed vs. accuracy. Specifically, when using the same number of 50 ODE steps during sampling, DiTMC+aPE-B is almost 5 times faster than ET-Flow-SS and surpasses ET-Flow-SS in all metrics on GEOM-DRUGS (see Table R1).

Table R1: Comparison of DiTMC+aPE-B to ET-Flow-SS on GEOM-DRUGS. -R indicates Recall, -P indicates Precision. Number of parameters in brackets. Final row shows relative improvement of DiTMC+aPE-B over ET-Flow-SS. A positive percentage indicates an improvement by DiTMC+aPE-B over the ET-Flow-SS baseline.

Table R2: Out-of-distribution generalization results on GEOM-XL. The ET-Flow paper does not report ET-Flow-SS on GEOM-XL, such that we stick to ET-Flow. Final row shows relative improvement of DiTMC+aPE-B over the ET-Flow baseline.

Moreover, DiTMC+aPE-B also outperforms ET-Flow-SS for smaller acceptance thresholds by a significant margin (see Table R3), a regime that is particularly relevant for many real-world applications, as it reflects the model’s ability to generate highly accurate conformations. Notably, ET-Flow-SS has been long-regarded as the best-in-class model for small acceptance thresholds. We believe that surpassing it represents a significant advance.

Table R3: Comparison of coverage (COV) metrics for DiTMC+aPE-B to ET-Flow-SS with a RMSD threshold of 0.10Å on GEOM-DRUGS. Final row shows relative improvement of DiTMC+aPE-B over the ET-Flow-SS baseline.

Overall, these experiments clearly demonstrate a significant performance improvement compared to ET-Flow-SS even for our base model of equal size. We will update and extend our final manuscript accordingly. Further, we will add information about the number of parameters of the large models in the main text for better comparison. We would be grateful if these points could be taken into account in the final assessment of our work.

The scalability of the proposed architecture is not clear. According to Fig. 3, increasing the number of parameters by four times does not yield the expected performance improvement, which may raise concerns about the model’s scalability.

1. Could the authors provide a more complete study over the scaling of the proposed approach by considering more model size?

Scaling our model from base to the large variant yields relative improvement in precision metrics between 3.5% (COV Mean) and 12.4% (AMR Median) (see Table A10 in the submitted manuscript). We obtain a relative improvement in terms of generalization to larger molecules by 3.1% to 7.3%, i.e. our large model exhibits significantly stronger out-of-distribution performance compared to the base model (see Table R4).

Table R4: Out-of-distribution generalization results on GEOM-XL when scaling our model. Final row shows relative improvement of aPE-L over aPE-B.

Scaling the base (“B”) to the large model (“L”) improves performance, but less than might be expected. Ref. [1] shows that to avoid diminishing returns, dataset and model sizes must be scaled together. Scaling only the model yields limited benefits.

To investigate this effect, we have trained an additional smaller (1M params) variant of our aPE model (“S”) to compare its performance to our aPE-B model (9.5M params). We obtain strong relative improvements up to 54.1% for coverage precision with aPE-B (see Table R5). This clearly shows that scaling is effective until model size saturates given the data. Our base model appears close to saturation and more data is needed to fully leverage the larger model’s potential. We hope this highlights the strength of our scaling results and resolves the reviewer’s Q1.

Table R5. Benefit of scaling for DiTMC+aPE on GEOM-DRUGS. Final row shows relative improvement of aPE-B over aPE-S.

[1] Kaplan, Jared, et al. "Scaling laws for neural language models." arXiv preprint arXiv:2001.08361 (2020).

The paper could be further improved by making the study more systematic. “… I believe a more comprehensive evaluation would be beneficial, for example, on 3D molecule generation or molecular property prediction tasks”

We agree that assessing the broader applicability of our architecture is important. Our primary goal was to introduce and analyze a novel framework for conformer prediction, a task with distinct structural challenges. To ensure a systematic study, we ablated key components, including conditioning strategies, positional embeddings, attention variants, and prior distributions, within this domain. We also examined scaling behavior on in- and out-of-distribution tasks using diverse metrics, including ensemble property prediction. We chose this scope to provide controlled and interpretable insights. We hope this clarification helps convey the systematic nature of our study and addresses the raised concerns.

The technical novelty is limited. While I appreciate the efforts to adapt DiT to molecular graphs, from a methodological perspective, the contribution is relatively minor.

While our approach builds upon a model architecture originally developed for the perceptual domain of computer vision, the successful adaptation to the domain of physically accurate molecular conformer generation required non-obvious and technically meaningful modifications, far from a straightforward transfer. Specifically, we solve the following, domain-specific challenges:

• We introduce a novel GNN-based conditioning mechanism to incorporate molecular graph information, which we show is crucial for conformer generation (Appendix H). Our approach departs from the global or text-based conditioning typical of image-based DiTs by leveraging both node-wise and pair-wise conditioning strategies (applied to atoms, bonds, or all atom pairs). We find and highlight significant differences in effectiveness among these strategies in our ablation experiments (Appendix Table A8).
• As part of this framework, we propose using geodesic graph distances as conditioning information. We are not aware of any other approach that uses geodesics (shortest paths) on the graph to condition the self-attention mechanism operating on the molecular geometry in 3D space. We have added a dedicated ablation (Table R6) to validate the impact of this component, showing that it is critical to the competitive performance of DiTMC.
• Finally, we investigate the role of incorporating physical symmetries (translations and rotations) into the model. We discuss the trade-offs between fidelity and computational cost when dealing with the 3D nature of molecular data in accordance with geometric principles.

Our ablation studies (Appendix E-H, K) and Table R6 demonstrate that removing any of the proposed modifications to the original DiT architecture leads to a substantial performance drop.

Table R6. Ablating the effects of our proposed conditioning strategy via graph geodesics on GEOM-DRUGS.

We would like to thank the reviewer for taking the time to carefully read our submitted manuscript and the overall positive assessment of our work. In the following, we comment on the points and questions raised by the reviewer.

Results for ensemble properties (Table 3) are compelling, though in E.3 it is described that this is after conformer relaxation with GFN2-xTB (this may be standard, but is still a limitation for practical use).

We fully agree that this can pose a limitation in practical use cases, i.e. when the system size starts to introduce computational overhead due to the necessity of applying quantum mechanical methods. Within our experiment, we follow this procedure for consistency with prior work. To acknowledge this practical limitation we will add it to the “Discussion & Limitations” section of our final manuscript.

Motivation: I'm not sure that the “encod[ing of] molecular connectivity and incorporat[ing] Euclidean symmetries, such as translational and rotational invariance/equivariance” is such a major challenge as posed, though, again, the formulation of the architectural components is extensive. Equivariant transformer architectures, e.g., Equiformer have existed for several years specifically for molecular generation, which incorporate many of the components necessary. Equivariant diffusion mechanisms for 3D molecule generation, e.g., EDM, GeoLDM, GeoBFN and the like have also been well demonstrated for conformer generation, though not necessarily conditioned on graph structure as proposed or with transformers (that I know of), which is nice and, yes, challenging. Equivariant, graph-conditioned conformer generation architectures do exist, e.g., MoleCLUEs, though again not with DiTs.

We agree that the concept of equivariant transformers as well as ideas around equivariant diffusion mechanisms are already established within the community. As correctly pointed out by the reviewer, one of the technical novelties lies in the conditioning on graph structure via geodesics, enabling the clean separation of graph structure and the operation in Euclidean space.

We will clarify and change our formulation in the abstract and also add a section in the related work part, which relates our approach to equivariant transformer and diffusion models. This hopefully enables the reader to better locate our approach in the overall landscape of equivariant transformer architectures and diffusion models.

The formulation modeling a velocity, i.e., vector field looks very similar to neural force fields, which is not super novel, though again the utilization of DiTs for this task is interesting.

Indeed, the output of our model (a 3-dimensional velocity vector per atom) resembles the structure of neural force fields which output atomic forces, which are also 3-dimensional vectors. In particular, the ET-Flow model takes great inspiration from the TorchMDNet model, which is an equivariant message passing neural network originally designed for neural force fields. Notably, our DiTMC models outperform the ET-Flow model even for the same number of parameters (see Table R1 and Table R2 below). This observation might hint to the fact that although input and output in both settings are structurally similar, generative models can benefit from additional architectural design choices as the ones made in our DiT architecture.

Table R1: Comparison of DiTMC+aPE-B to ET-Flow-SS on GEOM-DRUGS. -R indicates Recall, -P indicates Precision. Number of parameters in brackets. Final row shows relative improvement of DiTMC+aPE-B over ET-Flow-SS. A positive percentage indicates an improvement by DiTMC+aPE-B over the ET-Flow-SS baseline.

Table R2: Out-of-distribution generalization results on GEOM-XL for models trained on GEOM-DRUGS. -R indicates Recall, -P indicates Precision. Number of parameters in brackets. Final row shows relative improvement of DiTMC+aPE-B over ET-Flow. A positive percentage indicates an improvement by DiTMC+aPE-B over the ET-Flow baseline.

… discussion or experimentation on the effects of noise scheduling in the diffusion process, as this is expected to play a significant role in model fidelity

The choice of noise schedule mainly impacts the fidelity of generated samples via discretization error of the underlying ODE. It is therefore expected that most noise schedules converge to the same or very similar results in the limit of sufficiently small time steps, as is for example demonstrated in [1]. We find that evaluating our models with more steps doesn’t significantly change the results (see Table R3 below as an example), which likely means that we already hit that limit and won’t additionally benefit from a different schedule.

Table R3: Performance on GEOM-DRUGS for DiTMC+aPE-B with 50 and 100 ODE sampling steps. -R indicates Recall, -P indicates Precision.

[1] Karras, Tero, et al. "Elucidating the design space of diffusion-based generative models." Advances in neural information processing systems 35 (2022): 26565-26577.

Was a pairwise-distance positional embedding considered?

Yes, we also investigated a relative positional encoding strategy. We analyzed its performance on the QM9 dataset and found the results to be in line with the results for aPE and PE(3) (see Table 1 in the original manuscript). For the following experiments on GEOM-DRUGS we only kept the simplest aPE and the most evolved PE(3) strategies. For consistency, we additionally trained an rPE-B model on GEOM-DRUGS and report the results in Table R4 below.

Table R4: Results on GEOM-DRUGS for different DiTMC variants. -R indicates Recall, -P indicates Precision.

I must have missed somewhere, what is used as the prior (t=0) for each sample, i.e., where is the initial conformer obtained from?

We employ a Harmonic prior, following Ref. [2], as described in Section 5 of the experiments. To assess the impact of this choice, we also evaluate a more conventional Gaussian prior as an alternative in Appendix F.2 (see Table A15). Notably, our models perform remarkably well even when using a Gaussian prior, which is in contrast to the findings of the authors of ET-Flow. We believe that this highlights the effectiveness of our proposed conditioning strategies and the use of geodesic graph distances as conditioning information.

[2] Stärk, Hannes, et al. "Harmonic Self-Conditioned Flow Matching for Multi-Ligand Docking and Binding Site Design." CoRR (2023).

More details in the main text on how ensembles are generated, e.g., via rollout of different trajectories, would be appreciated, …

How are ensembles obtained? I.e., what does the rollout of parallel trajectories entail?

We adopt the property prediction task setup from MCF and ET-Flow, where we draw a subset of 100 randomly sampled molecules from the test set of GEOM-DRUGS and generate min(2K, 32) conformers for a molecule with K ground truth conformers. Afterwards we relax the conformers using GFN2-xTB and compare the Boltzmann-weighted properties of the generated and ground truth ensembles. More specifically, we employ xTB to calculate the energy $E$, the dipole moment $\mu$, the HOMO-LUMO gap $\Delta \epsilon$ and the minimum energy $E_{\text{min}}$. We repeat this procedure for three subsets each sampled with a different random seed and report the averaged median absolute error and standard deviation of the different ensemble properties.

In our DiTMC framework, we employ deterministic ODE sampling within the Flow Matching formalism. In the absence of integration errors, the integration path for each sample is therefore uniquely defined by the prior sample. However, we can still generate multiple samples for the same or even different molecules in parallel, by drawing multiple samples from the prior and combining the corresponding graphs into a larger graph with many isolated partitions (batching).

We will add the additional information, discussing the generation of ensembles, to the main text of our manuscript.