# MOFFlow: Flow Matching for Structure Prediction of Metal-Organic Frameworks

arXiv: https://arxiv.org/abs/2410.17270 · HTML: https://mlsanity.com/paper/2410.17270/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 73 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Equivariant Flow Matching with Hybrid Probability Transport](https://mlsanity.com/paper/2312.07168/) (2023)
- [An End-to-End Framework for Molecular Conformation Generation via Bilevel Programming](https://mlsanity.com/paper/2105.07246/) (2021)
- [An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties](https://mlsanity.com/paper/2005.07609/) (2020)
- [Improved motif-scaffolding with SE(3) flow matching](https://mlsanity.com/paper/2401.04082/) (2024)
- [Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functions](https://mlsanity.com/paper/2110.05064/) (2021)
- [Data-Driven Approach to Encoding and Decoding 3-D Crystal Structures](https://mlsanity.com/paper/1909.00949/) (2019)
- [Towards Symmetry-Aware Generation of Periodic Materials](https://mlsanity.com/paper/2307.02707/) (2023)
- [MOFDiff: Coarse-grained Diffusion for Metal-Organic Framework Design](https://mlsanity.com/paper/2310.10732/) (2023)

## Built on by (most cited first, 17 of 17)

- [Riemannian Variational Flow Matching for Material and Protein Design](https://mlsanity.com/paper/2502.12981/) (2025)
- [High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Prediction](https://mlsanity.com/paper/2505.18817/) (2025)
- [Materials Generation in the Era of Artificial Intelligence: A Comprehensive Survey](https://mlsanity.com/paper/2505.16379/) (2025)
- [Flexible MOF Generation with Torsion-Aware Flow Matching](https://mlsanity.com/paper/2505.17914/) (2025)
- [The Rise of Generative AI for Metal-Organic Framework Design and Synthesis](https://mlsanity.com/paper/2508.13197/) (2025)
- [Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion](https://mlsanity.com/paper/2502.09890/) (2025)
- [MolCrystalFlow: Molecular Crystal Structure Prediction via Flow Matching](https://mlsanity.com/paper/2602.16020/) (2026)
- [Generative Models for Crystalline Materials](https://mlsanity.com/paper/2511.22652/) (2025)
- [Latent Riemannian Flow Matching for Geometry-Grounded 3D Foundation Models](https://mlsanity.com/paper/2607.19120/) (2026)
- [LEGO-MOF: Equivariant Latent Manipulation for Editable, Generative, and Optimizable MOF Design](https://mlsanity.com/paper/2604.13520/) (2026)
- [Interpretable Inverse Design of Metal-Organic Frameworks with Large Language Model Agents](https://mlsanity.com/paper/2606.29459/) (2026)
- [Large language model agents accelerate inverse design of metal-organic frameworks for gas separation](https://mlsanity.com/paper/2607.10559/) (2026)
- [Packora: Systematic Design for Generative Molecular Crystal Structure Prediction](https://mlsanity.com/paper/2608.26962/) (2026)
- [GLASS: Global Latent Aggregation with Slot-based Set Decoding for Scalable All-Atom Crystal Generation](https://mlsanity.com/paper/2609.37158/) (2026)
- [Riemannian Flow Models with Reinforcement Learning for Molecular Crystal Structure Prediction](https://mlsanity.com/paper/2609.39773/) (2026)
- [Equivariant Flow Matching for Electron Density Prediction](https://mlsanity.com/paper/2610.02651/) (2026)
- [AnchorPose for Geometry-Aware MOF Assembly through Meso-Grained Pose Generation](https://mlsanity.com/paper/2610.05843/) (2026)

## Abstract (arXiv)

Metal-organic frameworks (MOFs) are a class of crystalline materials with promising applications in many areas such as carbon capture and drug delivery. In this work, we introduce MOFFlow, the first deep generative model tailored for MOF structure prediction. Existing approaches, including ab initio calculations and even deep generative models, struggle with the complexity of MOF structures due to the large number of atoms in the unit cells. To address this limitation, we propose a novel Riemannian flow matching framework that reduces the dimensionality of the problem by treating the metal nodes and organic linkers as rigid bodies, capitalizing on the inherent modularity of MOFs. By operating in the SE(3) space, MOFFlow effectively captures the roto-translational dynamics of these rigid components in a scalable way. Our experiment demonstrates that MOFFlow accurately predicts MOF structures containing several hundred atoms, significantly outperforming conventional methods and state-of-the-art machine learning baselines while being much faster.