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MOFFlow: Flow Matching for Structure Prediction of Metal-Organic Frameworks
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Introduces MOFFlow, a Riemannian flow matching model over SE(3) block roto-translations and lattice parameters that predicts MOF crystal structures from building blocks.
Problem
Predicting crystal structures of metal-organic frameworks, which have hundreds to thousands of atoms per unit cell, is too expensive for DFT-based search and fails for existing general crystal structure generative models.
Approach
Treat MOF metal nodes and organic linkers as rigid bodies and generate their SE(3) roto-translations plus lattice parameters with Riemannian flow matching, using a new MOFAttention module (an invariant-point-attention variant that adds lattice parameters as attention offsets), reducing dimensionality from 3N atomic coordinates to 6M block degrees of freedom.
Key results
- MOFFlow reaches 31.69% match rate with 1 sample at stol=0.5 vs 0.09% for DiffCSP (1 sample) and 0% for RS/EA; 44.75% with 5 samples.
- MOFFlow averages 1.94 s per structure for one sample versus 5.37 s for DiffCSP.
- MOFFlow maintains high match rate on structures beyond 1,000 atoms while DiffCSP fails to predict structures above 200 atoms.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use building-block-based MOFFlow instead of atom-based DiffCSP | MOF structure prediction · MOF test set, stol=0.5, 1 sample | match rate (%): 0.09 -> 31.69 | Helped |
| use building-block-based MOFFlow instead of atom-based DiffCSP | MOF structure prediction · MOF test set, stol=0.5, 1 sample | RMSE: 0.3961 -> 0.2820 | Helped |
| use building-block-based MOFFlow instead of atom-based DiffCSP | MOF structure prediction · MOF test set, stol=0.5, 1 sample | average generation time: 5.37 -> 1.94 | Helped |
| use building-block-based MOFFlow instead of RS or EA | MOF structure prediction · MOF test set, stol=0.5 | match rate (%): 0.00 -> 31.69 | Helped |
| use standard multi-instance Batch instead of TimestepBatch (ablation) | MOFFlow · MOF test set | training time (h): 1087.25 -> 332.74 | Helped |
| use standard multi-instance Batch instead of TimestepBatch (ablation) | MOFFlow · MOF test set | inference time (s): 1.94 -> 0.1932 | Helped |
| use standard multi-instance Batch instead of TimestepBatch (ablation) | MOFFlow · MOF test set, stol=0.5 | match rate (%): 31.69 -> 32.73 | Helped |
| replace learned rotations with self-assembly rotations (ablation) | MOFFlow using predicted translations and lattice · MOF test set | match rate (%): 31.69 -> 30.04 | Hurt |
| replace learned rotations with self-assembly rotations (ablation) | MOFFlow using predicted translations and lattice · MOF test set | inference time (s): 1.94 -> 4.75 | Hurt |
| increase sampling integration steps from 50 to higher step counts (ablation) | MOFFlow · MOF test set | match rate | Hurt |
Surprising findings
- Optimization-based methods (RS, EA) achieve zero match rate on MOFs, and DiffCSP performs poorly, showing atom-based approaches fail at MOF scale.
- The self-assembly algorithm scales better than MOFFlow for structures with more building blocks, despite MOFFlow's higher overall match rate.
Limitations
- Evaluated only on the hypothetical MOF database, not real-world MOFs.
- Assumes building block local structures are known (rigid-body assumption), which may fail for rare or missing building blocks.
- Not invariant to periodic transformations of the input.
Experimental setup
Datasets: hypothetical MOF database (324,426 structures)
Benchmarks: hypothetical MOF test split (30,880 structures)
Metrics: match rate RMSE inference time zeo++ property RMSE
Baselines: RS (CrySPY) EA (CrySPY) DiffCSP self-assembly algorithm
Builds on: Riemannian flow matching DiffCSP invariant point attention FrameFlow
Closest papers by meaning
- Flexible MOF Generation with Torsion-Aware Flow Matching (NeurIPS 2025 · similarity 0.93)
- MOFDiff: Coarse-grained Diffusion for Metal-Organic Framework Design (ICLR 2024 · similarity 0.91)
- Fast Organic Crystal Structure Prediction with Unit Cell Flow Matching (NeurIPS 2026 · similarity 0.87)
- Swallowing the Bitter Pill: Simplified Scalable Conformer Generation (ICML 2024 · similarity 0.86)
- FlowMM: Generating Materials with Riemannian Flow Matching (ICML 2024 · similarity 0.86)
- 3D Structure Prediction of Atomic Systems with Flow-based Direct Preference Optimization (NeurIPS 2024 · similarity 0.85)
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