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Unified Generative Modeling of 3D Molecules with Bayesian Flow Networks
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Introduces GeoBFN, a Bayesian Flow Network adapted to 3D molecule geometry that models continuous coordinates, discretised charges and categorical atom types in parameter space with SE(3)-invariant density, achieving state-of-the-art QM9 and GEOM-DRUG unconditional generation and faster sampling.
Problem
Applying diffusion models to 3D molecule geometry is hard due to multi-modality (continuous coordinates plus discrete atom types/charges) and noise sensitivity of coordinates, where small perturbations break molecular structure.
Approach
Adapt Bayesian Flow Networks to molecular geometry: perform noising and generation in the parameter space of factorised distributions (Gaussian for coordinates and charges, softmax for atom types), use an EGNN output network to keep SE(3)-invariant density, and use nearest-center mode-seeking sampling for discretised charges, enabling any-step sampling with lower-variance trajectories.
Key results
- GeoBFN with 1k steps reaches 90.87% molecule stability on QM9 and 85.60% atom stability on GEOM-DRUG, exceeding GeoLDM's 89.4% and EDM's 82.0% on QM9.
- GeoBFN with 50 steps already outperforms several baselines, giving about a 20x speedup in sampling.
- On conditional QM9 generation with 500 steps, GeoBFN achieves lower MAE than GeoLDM on all six properties (e.g., alpha 2.34 vs 2.37).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use GeoBFN instead of GEOLDM | 3D molecule generation · QM9 | molecule stability: 89.4 ± 0.5 -> 90.87 | Helped |
| use GeoBFN instead of GEOLDM | 3D molecule generation · GEOM-DRUG | atom stability: 84.4 -> 85.60 | Helped |
| use GeoBFN instead of GEOLDM | conditional molecule generation · QM9 | MAE α: 2.37 -> 2.34 | Helped |
| use GeoBFN instead of GEOLDM | conditional molecule generation · QM9 | MAE Δε: 587 -> 577 | Helped |
| use GeoBFN instead of GEOLDM | conditional molecule generation · QM9 | MAE ε_HOMO: 340 -> 328 | Helped |
| use GeoBFN instead of GEOLDM | conditional molecule generation · QM9 | MAE ε_LUMO: 522 -> 516 | Helped |
| use GeoBFN instead of GEOLDM | conditional molecule generation · QM9 | MAE μ: 1.108 -> 0.998 | Helped |
| use GeoBFN instead of GEOLDM | conditional molecule generation · QM9 | MAE C_v: 1.025 -> 0.949 | Helped |
| sample with 50 rather than 1k steps | GeoBFN · QM9 | molecule stability: 90.87 -> 85.11 | Hurt |
| replace discretised basis charge with continuous basis charge (ablation) | GeoBFN · QM9 | molecule stability: 90.87 -> 89.94 | Hurt |
| replace discretised basis charge with discrete atom types (ablation) | GeoBFN · QM9 | molecule stability: 90.87 -> 88.93 | Hurt |
| add discrete atom types and continuous charge (ablation) | GeoBFN · QM9 | molecule stability: 90.87 -> 89.33 | Hurt |
Surprising findings
- Using only the discretised charge variable (without one-hot atom types) gave better stability than including the discrete atom-type representation in the ablation.
Limitations
- Reported results use 1k sampling steps for fair comparison; gains depend on sampling steps and may improve with longer sampling.
- Atom-type and charge representation choices affect performance, and discrete atom types were found to hurt in ablation.
- Hardware and training compute are not reported.
Experimental setup
Datasets: QM9 GEOM-DRUG
Benchmarks: QM9 GEOM-DRUG
Metrics: atom stability molecule stability validity validity x uniqueness novelty mean absolute error
Baselines: G-Schnet ENF GDM-aug EDM EDM-Bridge GeoLDM
Builds on: Bayesian Flow Networks EDM EGNN
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