Title: MOF-BFN: Metal-Organic Frameworks Structure Prediction via Bayesian Flow Networks
Venue: NeurIPS 2025
Accepted: yes
Keywords: Metal-Organic Frameworks

Bayesian Flow Networks

Material Design
Abstract: Metal-Organic Frameworks (MOFs) have attracted considerable attention due to their unique properties including high surface area and tunable porosity, and promising applications in catalysis, gas storage, and drug delivery. Structure prediction for MOFs is a challenging task, as these frameworks are intrinsically periodic and hierarchically organized, where the entire structure is assembled from building blocks like metal nodes and organic linkers. To address this, we introduce MOF-BFN, a novel generative model for MOF structure prediction based on Bayesian Flow Networks (BFNs). Given the local geometry of building blocks, MOF-BFN jointly predicts the lattice parameters, as well as the positions and orientations of all building blocks within the unit cell. In particular, the positions are modelled in the fractional coordinate system to naturally incorporate the periodicity. Meanwhile, the orientations are modeled as unit quaternions sampled from learned Bingham distributions via the proposed Bingham BFN, enabling effective orientation generation on the 4D unit hypersphere. Experimental results demonstrate that MOF-BFN achieves state-of-the-art performance across multiple tasks, including structure prediction, geometric property evaluation, and de novo generation, offering a promising tool for designing complex MOF materials.


Peer reviews:
comments: SUMMARY:
The authors of this paper address the challenging task of structure prediction for Metal-Organic Frameworks (MOFs). They highlight the intrinsic complexities of the problem and the limitations of existing models such as CDVAE, DiffCSP, MOFFlow, and CrysBFN. To overcome these challenges, they propose Bayesian Flow Networks (BFNs) and introduce MOF-BFN, a novel generative framework for hierarchical MOF structure prediction based on this approach.

STRENGTHS AND WEAKNESSES:
**Strength:**
 - The paper is well-written and easy to follow, with a clearly motivated problem and sufficient background information to support the study.
- Overall methodology is novel. MOF-BFN operates in the fractional coordinate system to preserve periodicity. Also they models block orientations using unit quaternions sampled from Bingham BFNs—a novel generative module.
- The experimental setup of the paper is solid, Authors have experimented with 	state-of-the-art models on benchmark material generation tasks.
- Source code is available

**Weakness:**
- Many relevant works on Crystal generations are missing FlowLLM, TGDMat, SymmSD, DiffCSP++
- A recent ICLR work, TGDMat[1], has demonstrated promising performance on the crystal structure prediction (CSP) task using text guidance with a single sample in a diffusion model. Could you please evaluate your model's performance under similar text-guided settings, or alternatively, report results on the BW-DB dataset using TGDMat (Long) for a fair comparison?
 						
[1] https://arxiv.org/abs/2503.00522

QUESTIONS:
Check weaknesses

LIMITATIONS:
Check weaknesses
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 4
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces MOF-BFN, the first framework for MOF structure prediction that jointly models periodicity, position, and orientation using a Bayesian Flow Network (BFN). It improves prior work by: \n1. Modeling periodicity explicitly using fractional coordinates\n2. Enhancing performance by leveraging Bayesian flow instead of flow matching \n\nIt also presents a technical contribution by extending BFN to model rotations. Experiments demonstrate superiority over existing approaches in both structure prediction and de novo generation tasks.\n\nSTRENGTHS AND WEAKNESSES:\n# Strengths\n- This is the first work to integrate SO(3) modeling within the BFN framework, offering a novel contribution by jointly modeling periodicity, lattice, and orientation for MOFs.\n- The method supports unconditional generation and explicitly handles periodicity, both of which are not well-addressed in previous work.\n\n# Weaknesses\n- Insufficient architectural detail: Section 4.3's \"Backbone Model for MOF-BFN\" provides only a high-level overview and lacks a self-contained explanation of the model architecture. Moreover, the method for determining the number of building blocks $K$ for de novo generation is not explained in Appendix C.\n- Potential computational inefficiency: While the method shows strong empirical performance, it likely incurs higher computational costs than flow-based methods due to the need for rejection sampling and posterior simulation over non-Euclidean spaces. A quantitative comparison of resource usage (e.g., training/inference time, memory, hardware) with baselines like MOF-FracFlow is necessary to assess trade-offs.\n\n## Typos and minor issues \n- Line 44: to jointly generates\n- Line 102: Represtations -> Representations \n- Footnote in page 3: represtation -> representation \n- Line 162: Incomplete sentence: “Initialized from the prior $\\mathbf{\\theta}_0^{\\mathcal{M}}$.”\n- Line 175: Bayesain -> Bayesian\n\nQUESTIONS:\n1. Have the authors considered comparing the training and inference costs of MOF-FracFlow and MOF-BFN under consistent settings (e.g., batch size, GPU type, total epochs)?\n2. Could the authors give a more detailed breakdown of the model architecture? Also, how is the number of building blocks $K$ determined during de novo generation?\n3. How does the model size of MOF-BFN compare to MOFFlow and MOFFrac-Flow (e.g., number of parameters)?\n4. Line 210-211 mentions that $M_0$ is an arbitrary orthogonal matrix. Could the authors elaborate on this?\n5. While the benefits of BFN are acknowledged, could the authors comment on the potential drawbacks of Bayesian flow (e.g., stability, scalability) compared to flow matching or diffusion? This question is asked purely out of curiosity.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces MOF-BFN, a generative model for predicting the structures of Metal-Organic Frameworks (MOFs) using Bayesian Flow Networks (BFNs). MOF-BFN leverages the local geometry of metal nodes and organic linkers to jointly predict lattice parameters, as well as the positions (in fractional coordinates) and orientations (via unit quaternions) of building blocks within a periodic unit cell. The model uses a Bingham BFN to effectively sample orientations on the 4D unit hypersphere. Experiments show MOF-BFN achieves strong performance in structure prediction, geometric property evaluation, and de novo MOF generation.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The paper tackles the complex task of MOF structure generation using Bayesian Flow Networks, extending the paradigm to a challenging problem.\n2. The paper has a sound modeling strategy and architecture design; the use of fractional coordinates and BFNs provides a novel alternative to conventional ODE and SDE-based models. The model appropriately incorporates relevant symmetries, improving its ability to handle the periodic nature of MOFs.\n3. The model is compared against relevant baselines and demonstrates strong performance across the reported metrics, highlighting its effectiveness relative to existing approaches.\n\nWeaknesses:\n\n1. The paper does not discuss the diversity or uniqueness of the generated MOF structures. It remains unclear whether the model generates topologies that are distinct from those in the training set.\n2. There is no analysis of whether the generated structures deviate in terms of geometric or physical properties (e.g., as shown in Table 2) from the training data. A meaningful distribution shift is often a desirable characteristic in generative models, as it indicates the ability to explore novel and diverse regions of the design space.\n3. The de novo generation results focus on structural validity rather than novelty. However, novelty is a central goal of de novo design and should be explicitly evaluated and discussed.\n4. The authors do not adequately address the limitations of their method. Given the complexity of MOF generation and the relatively modest validation rates, it is important to acknowledge the method’s current boundaries and potential areas for improvement.\n\nQUESTIONS:\n1. How diverse are the generated MOF structures? Can you provide an analysis showing whether the generated topologies differ significantly from those in the training dataset?\n2. Have you evaluated whether the distribution of geometric and physical properties in the generated structures shifts relative to the training set? If so, can you discuss the implications of any observed shifts?\n3. Could you elaborate on the novelty aspect of your de novo generation results? How do you measure or ensure that newly generated structures represent novel topologies rather than variants of known ones?\n4. What are the main limitations of your approach, particularly regarding generation validity rates and scalability? How might these limitations affect the applicability of MOF-BFN in real-world MOF design tasks?\n\nLIMITATIONS:\nSection Missing", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors introduce a novel way of parameterizing a joint lattice-position-orientiation distribution of hierarchical MOF structures. By simultaneously learning the bayesian flow distributions of the lattice parameters in R^6,  the fractional coordinates represented by elements of the torus T^3 (times the number of bodies), and the bingham distribution on the unit quaternions (again times the number of bodies), the authors demonstrate the ability to generate better structures compared to several baselines.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: \n-The paper is straightforward to read and understand, and offers a clearly novel idea for learning to sample hierarchical MOF structures. The results demonstrate clear improvement over existing approaches.\n\n-The authors use a clever conjugate relationship to enable bayesian flow distribution to be defined on the unit quaternions\n\nWeaknesses:\n-One thing i don’t fully understand is how widespread of a tool this would be for MOF researchers. I don’t fully understand the scope of problems this model can solve. Are there examples of this?\n\n-It seems like it would be eventually be useful to have some kind of MOF simulator (e.g. DFT) in the loop to provide effectively infinite data for the model to learn from. \n\n-Not sure how convincing the margin between MOFFlow and MOFBFN is.\n\nQUESTIONS:\n-Do there exist families of distributions on other Lie groups such as $SE(3)$? The nice thing about using the unit quaternions, which are specific to SO(3), is that the Bingham distribution defined on them has a nice conjugate relationship with the Watson distribution.\n\n-Could the role of $\\mathcal{L}_{\\mathcal{B}}$ be clarified for doing de novo generation? \n\n-How does the block representation of MOFFlow compare to the representation proposed in the paper? If they are different, which (between the block representation being used or the learning algorithm itself) is the dominant factor in model performance? \n\n-In general, what else is different between MOF-BFN and MOFFlow, and why would we expect that change to make MOF-BFN superior?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses Metal Organic Framework structure prediction and de novo generation. To tackle this, it leverages Bayesian Flow Networks that operate on a carefully selected MOF representation space, crucially, this space entails fractional coordinates, as well as orientations modeled as unit quaternions. These quaternions are parameterized via Bingham distributions.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths:\n- [Quality] The authors provide a theoretically sound approach to the representation of MOFs, which is further complemented by the selection of parameterization that contains key inductive biases connected to the application domain. The experimental results support the use of Bayesian Flow Networks, the proposed representations, and key parameterized distributions.\n- [Clarity] In general, the submission is well-structured, with precise and consistent notation that highlights the key design choices and theoretical motivations. The experimental setup is easy to follow, and the results are well-presented.\n- [Significance] MOF-BFN outperforms previous work, with selected representations that provide valuable insights for future work. Furthermore, it provides an overview of how to implement BFNs with the Bingham distribution. Therefore, it constitutes a meaningful achievement within the field\n- [Originality[ The authors cite relevant work, and their contributions are well-contextualized within the field of MOFs and broad material design. The contributions are novel.\n### Weaknesses:\n- [Quality] It is scientifically unclear which of the technical contributions leads to improved experimental results.\n- [Clarity] The large number of mathematical symbols makes reading and comprehension harder; Additionally, in the experimental section, it should be clear why only a subset of the external models are considered for each table/figure, please see my further remarks.\n- [Significance] I believe the paper would benefit from more extensive ablation studies. In particular, with respect to the selection of unit quaternions and the utilization of the Bingham distribution, instead of alternative representations and distributions\n\nQUESTIONS:\n- Could the authors elaborate on the choice of unit quaternions and the Bingham distribution? It would be helpful to see empirical evidence, such as additional ablation studies, to justify the contributions.\n\n- I am wondering if all four distinct hyperparameters are necessary to balance the loss function. Typically, such balancing is used when optimizing disparate training signals, whereas here each loss component appears to correspond to a core aspect of the representation.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-06"}