Flexible MOF Generation with Torsion-Aware Flow Matching

Dear reviewer eFsz,

We deeply appreciate your thorough review and constructive comments on our manuscript! We also appreciate your recognition of our work, including advancing generative modeling capabilities with torsional flexibility, extensive evaluations, and expansion of the design space with novel building blocks. Below, we address the reviewer's concerns and questions in detail.

W1. Insufficient discussion of computational cost and resource requirements (e.g., training cost, inference time). Include in the main text.

The training cost is detailed in Appendix A.2 and F.1, and the inference time is reported in Table 3 of the main text. For clarity, we summarize the key information below:

Due to space limitations, we follow common practice and have placed details on computational resources in the Appendix. However, to address your suggestion, we will refer to this information on line 294 (Section 6) of the main text.

W2. The stability of generated structures hasn't been evaluated with DFT or ab initio methods. Okay to leave for future work.

We appreciate your understanding! Nevertheless, to address your concern, we validate the energy of generated MOF structures using UMA [2], the state-of-the-art machine learning force field, which was verified to work on MOFs. While DFT would be ideal, it is computationally infeasible for large MOF structures within the rebuttal period and our computational budget.

Specifically, we generate 10,000 structures with MOFFlow-2 and MOFDiff and compute the energy per atom ($\mathrm{eV/atom}$) with the uma-m-1.1 model. As shown in the percentile table below, MOFFlow-2 consistently produces structures with lower energy levels compared to MOFDiff. We also plan to add histograms of energy levels in the future manuscript, which could not be included in the rebuttal due to NeurIPS rules.

W3. MOF is a specific family of molecules. Limited exploration of how the method scales/performs for significantly different MOF types or more diverse frameworks as an ML for science work.

While MOF is indeed a specific class of materials, we still believe our work has huge implications. MOFs are being investigated for many real-world problems, e.g., carbon capture, catalysis, or even drug delivery, and exhibit unique characteristics, e.g., modular nature, high-symmetry point groups, and the combination of organic and inorganic components, which require specialized algorithms.

We resonate with your point and consider generalization of our work to a broader domain, e.g., including new element types or applying our model to covalent organic frameworks, as a significant research direction. We note that, in principle, our work is generalizable to such new dataset without much modification.

Q1. Is the Boyd et al. dataset enough for learning the distribution of MOF structure? Will incorporating other data sources of large scale molecule/material datasets for pretraining help? Why or why not?

Since the Boyd et al. dataset [2] is a widely recognized MOF benchmark with diverse topologies and building blocks [3-5], we believe that it is a strong dataset for learning the distribution of MOFs. However, it may not fully capture the edge cases, such as rare element types in the broader MOF space.

Therefore, we believe that pretraining on large-scale molecular/material datasets can be beneficial, since the atoms in MOFs share the same fundamental interactions as in other molecules/materials. This strategy has proven effective in recent work (UMA [1]), and we expect similar benefits for our model.

Q2. In Table 2, under the smaller tolerance threshold (stol=0.3), why are the MR and RMSE between DiffCSP and MOFFlow-2 inconsistent?

This inconsistency arises because RMSE is calculated only on matched structures, meaning that DiffCSP performs worse than MOFFlow-2 when considering all the generated samples. DiffCSP has a very low match rate (~0.08%), so its RMSE is based on a small number of trivial matches, resulting in low RMSE. In contrast, MOFFlow-2 has a much higher match rate (~15.98%), and its RMSE is computed over a broader and more complex set of structures, resulting in a higher value.

Q3. What are the major differences between MOFFlow-1 and MOFFlow-2? What causes the performance gain in the structure prediction task in Table 2?

MOFFlow-2 mainly improves over MOFFlow-1 through (1) removing the rigid body assumption and (2) adding the ability to generate MOFs from scratch.

We make a one-by-one comparison as follows:

1. Rigid body assumption: MOFFlow-1 assembles MOF structures by treating building blocks as rigid bodies and thus requires their ground-truth conformations as input. In contrast, MOFFlow-2 relaxes this assumption by explicitly modeling torsional flexibility, allowing the building blocks to adjust their conformations during assembly.
2. Generative capability: MOFFlow-1 is designed solely for structure prediction and cannot generate new MOF structures. MOFFlow-2, on the other hand, supports both generation and prediction.

The performance improvement in the structure prediction task is mainly due to MOFFlow-2’s ability to model torsional flexibility, which accounts for conformational changes during the assembly.

Q4. How are validity, novelty, and uniqueness (in Figure 3, Table 3, Section 6.2) defined? I could not find the definition of these metrics.**

The definitions of validity, novelty, and uniqueness are defined in lines 331-333 of the main text. For your convenience, we restate the definition here.

• Validity (%): A generated MOF is valid if it passes the MOFChecker [6] test. This includes a basic sanity check for MOFs, such as the presence of metal and organic elements, porosity, no overlapping atoms, etc.
• Novelty (%): A structure is considered novel if its MOFid [7] does not appear in the training set. This essentially means that a MOF is novel if either a novel building block or a novel combination of building blocks has been used.
• Uniqueness (%): Uniqueness is the proportion of distinct structures after removing duplicates from the generated set.
• VNU (%) is defined as the proportion of generated structures that are simultaneously valid, unique, and novel.

Q5. Which degrees of freedom have not been modeled under the setting of MOFFlow-2?

MOFFlow-2 does not model bond angles and lengths, since RDKit accurately generates them. This is a widely accepted assumption [8, 9], which underpins many celebrated works on molecular generative models (e.g., Torsional diffusion [9], DiffDock [10], FlexDock [11]). While one could additionally model such degrees of freedom, we do not expect a meaningful improvement in accuracy despite the additional computational cost.

We hope our experiments address your questions and concerns! Please let us know if there are any further opportunities for clarification and improving the score.

Reference

[1] Wood, Brandon M., et al. "UMA: A Family of Universal Models for Atoms." arXiv preprint arXiv:2506.23971 (2025).
[2] Boyd, Peter G., et al. "Data-driven design of metal–organic frameworks for wet flue gas CO2 capture." Nature 576.7786 (2019): 253-256.
[3] Fu, Xiang, et al. "Mofdiff: Coarse-grained diffusion for metal-organic framework design." arXiv preprint arXiv:2310.10732 (2023).
[4] Wu, Xiaoyu, and Jianwen Jiang. "Precision-engineered metal–organic frameworks: fine-tuning reverse topological structure prediction and design." Chemical Science 15.40 (2024): 16467-16479.
[5] Liu, Yutao, et al. "Porous framework materials for energy & environment relevant applications: A systematic review." Green Energy & Environment 9.2 (2024): 217-310.
[6] Jablonka, K. M. (2023). mofchecker (Version 1.0.0) [Computer software]. https://doi.org/10.5281/zenodo.1234
[7] Bucior, Benjamin J., et al. "Identification schemes for metal–organic frameworks to enable rapid search and cheminformatics analysis." Crystal Growth & Design 19.11 (2019): 6682-6697.
[8] Axelrod, Simon, and Rafael Gomez-Bombarelli. "GEOM, energy-annotated molecular conformations for property prediction and molecular generation." Scientific Data 9.1 (2022): 185.
[9] Jing, Bowen, et al. "Torsional diffusion for molecular conformer generation." Advances in neural information processing systems 35 (2022): 24240-24253.
[10] Corso, Gabriele, et al. "DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking." International Conference on Learning Representations (ICLR 2023). 2023.
[11] Corso, Gabriele, et al. "Composing unbalanced flows for flexible docking and relaxation." The Thirteenth International Conference on Learning Representations. 2025.

We’re glad to hear that our response addressed your questions and concerns! Thank you also for your kind words and support for our work. We truly appreciate your constructive feedback throughout the review process, which has helped us improve the overall quality of our work.

Dear reviewer Figq,

We deeply appreciate your thorough review and constructive comments on our manuscript! We also appreciate your recognition of our work, including the effectiveness of our two-stage approach and improved empirical results. Below, we address the reviewer's concerns and questions in detail.

W1. I think the evaluation is still limited, and the authors compared to classical methods and a few baselines like MOFDiff.

We consider our set of baselines to be comprehensive, given how the MOF generative model is an under-explored research area. We note that MOFFlow-1 and MOFDiff are among the first deep learning models that can generate MOFs from scratch. MOFDiff itself had no learning-based baselines for similar reasons.

We also note that classical methods like random search (RS) and evolutionary algorithms (EA) are strong and widely used baselines in the crystal structure prediction (CSP) field, making them meaningful baselines for comparison.

If you have any suggestions for the baselines, we would be happy to incorporate them.

W2. Method relies on a bioinformatics tool like RDKit for initial structure generation, and assumes that the initial bond lengths and angles are accurate.

We do not think this is a weakness of our method, as the bond lengths and angles generated by cheminformatics toolkits are widely accepted to be accurate and accessible [1, 2]. Our algorithm re-initializes the remaining structure (torsion) and does not depend on highly variable information. Also, the reliance on RDKit for estimating the bond lengths and angles underpins many celebrated works on molecular generative models (e.g., Torsional diffusion [2], DiffDock [3], FlexDock [4]).

Q1. Did you investigate the model's sensitivity to the quality of RDKit-generated conformers?

Yes; MOFFlow-2 is robust to the quality of RDKit-generated conformers, since it relies only on the bond lengths and angles, which RDKit reliably estimates. While RDKit may be inaccurate for torsion angles, our model is insensitive to this since it randomly reinitializes them at $t=0$.

To empirically confirm this, we evaluate our model on four sets of initial conformers randomly generated by RDKit, given the same building blocks. As shown below, the performance remains consistent, with negligible variation in both validity and VNU metrics:

We hope our experiments address your questions and concerns! Please let us know if there are any further opportunities for clarification and improving the score.

Reference

[1] Axelrod, Simon, and Rafael Gomez-Bombarelli. "GEOM, energy-annotated molecular conformations for property prediction and molecular generation." Scientific Data 9.1 (2022): 185.
[2] Jing, Bowen, et al. "Torsional diffusion for molecular conformer generation." Advances in neural information processing systems 35 (2022): 24240-24253.
[3] Corso, Gabriele, et al. "DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking." International Conference on Learning Representations (ICLR 2023). 2023.
[4] Corso, Gabriele, et al. "Composing unbalanced flows for flexible docking and relaxation." The Thirteenth International Conference on Learning Representations. 2025.

Dear reviewer EcT6,

We deeply appreciate your thorough review and constructive comments on our manuscript! We also appreciate your recognition of our work, including clear motivation and reasonable contribution, substantial empirical improvements, and good writing clarity. Below, we address the reviewer's concerns and questions in detail.

W1. Lack of physical validation.

To address your concern, we validate the energy of generated MOF structures using UMA [1], the state-of-the-art machine learning force field, which was verified to work on MOFs. While DFT would be ideal, it is computationally infeasible for large MOF structures within the rebuttal period and our computational budget.

Specifically, we generate 10,000 structures with MOFFlow-2 and MOFDiff and compute energy per atom ($\mathrm{eV/atom}$) with the uma-m-1.1 model. As shown in the percentile table below, MOFFlow-2 consistently produces structures with lower energy levels compared to MOFDiff. We also plan to add histograms of energy levels in the future manuscript, which could not be included in the rebuttal due to NeurIPS rules.

W2. The framework does not demonstrate property-driven generation scenarios.

We appreciate the reviewer’s insightful comment. Our method can be easily extended to property-driven generation, and here we demonstrate this by generating MOFs to maximize CO2 working capacity. To this end, we (1) train MOFFlow-2 conditioned on CO2 working capacity and (2) generate MOFs conditioned on sufficiently high values of this property.

To be specific, we re-train the building block generator to cross-attend to working capacity $y$ featurized as $c=\text{Linear}(y) + \text{Fourier}(y)$. During inference, we sample 200 building blocks conditioned on $y=4$ and compute the CO2 working capacity by running a grand canonical Monte Carlo (GCMC) simulation [2]. As shown in the table below, MOFFlow-2 successfully generates MOFs with high working capacity and outperforms MOFDiff. Note that MOFDiff applies latent optimization with a target of $y=15$.

We also plan to update our code and add working capacity histograms in the future manuscript, which could not be included in the rebuttal due to NeurIPS rules.

Q1. How sensitive is the performance of MOFFlow-2 to the initial RDKit geometries used for organic linkers?

MOFFlow-2 performs robustly regardless of initial RDKit geometries, since it relies only on the bond lengths and angles, which RDKit reliably estimates. While RDKit may be inaccurate for torsion angles, our model is insensitive to this since it randomly reinitializes them at $t=0$.

To empirically confirm this, we evaluate our model on four sets of initial conformers randomly generated by RDKit, given the same building blocks. As shown below, the performance remains consistent, with negligible variation in both validity and VNU metrics:

Q2. How well does the model generalize to MOF chemistries that are entirely out-of-distribution (OOD) from training?

Similar to any other machine learning algorithm, our method will struggle to generalize to data that is entirely out-of-distribution (OOD). For example, MOFFlow-2 is not capable of generalizing to unseen element types. Also, its performance for MOFs with complex topologies and many building blocks may be lower than those common in the dataset. However, this can be alleviated by training our model on a more diverse set of MOF/crystal structures (e.g., datasets from [3] or the Materials Project [4]).

We hope our experiments address your questions and concerns! Please let us know if there are any further opportunities for clarification and improving the score.

Reference

[1] Wood, Brandon M., et al. "UMA: A Family of Universal Models for Atoms." arXiv preprint arXiv:2506.23971 (2025).
[2] Fu, Xiang, et al. "Mofdiff: Coarse-grained diffusion for metal-organic framework design." arXiv preprint arXiv:2310.10732 (2023).
[3] Lee, Sangwon, et al. "Computational screening of trillions of metal–organic frameworks for high-performance methane storage." ACS Applied Materials & Interfaces 13.20 (2021): 23647-23654.
[4] Jain, Anubhav, et al. "Commentary: The Materials Project: A materials genome approach to accelerating materials innovation." APL materials 1.1 (2013).

@Reviewer EcT6: Please respond to authors rebuttal and update rating accordingly.

Dear reviewer qUfU,

We deeply appreciate your thorough review and constructive comments on our manuscript! We also appreciate your recognition of our work, including the novelty of our approach, strong experimental results, and clear methodology/architecture. Below, we address the reviewer's concern in detail.

W1. Insufficient ablation studies. Analyze the contribution of each component in the two-stage pipeline (e.g., the SMILES generator and flow matching) to the overall performance.

Thank you for your insightful comment. While our comparison of MOFFlow-2 and MOFFlow-1 in Table 2 ablates the effect of torsion flexibility for structure prediction, we provide more studies to resolve your concern. Our new results confirm that both (1) SMILES generation quality and (2) torsional flexibility modeling are important for MOF generation.

1. Varying SMILES generator quality: We first ablate the effect of the SMILES generator on the MOF generation quality. To this end, we train the SMILES generator with a varying number of steps and evaluate its quality with SMILES-VNU* (left column). Each is then paired with the same flow matching module, and the full pipeline is evaluated using VNU (right column). Results show that improvements in the SMILES generator directly lead to higher overall MOF quality.

*SMILES-VNU is the percentage of generated MOF sequences that are valid (RDKit sanity check), novel (not in training set), and unique (non-duplicated).

2. Excluding torsional flexibility: Next, we ablate the effect of torsional flexibility on the MOF generation quality. Replacing MOFFlow-2 with MOFFlow-1 (no torsion modeling) in the assembly stage clearly degrades the performance in MOF generation.

We hope our experiments address your concerns! Please let us know if there are any further opportunities for clarification and improving the score.

We’re happy to hear that the ablation studies addressed your concerns. Thank you as well for your kind support of our work. We truly appreciate your constructive comments throughout the review process, which have helped us improve the overall quality of our work.