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Score-based 3D molecule generation with neural fields
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Introduces FuncMol, which represents 3D molecules as continuous atomic occupancy neural fields and samples modulation codes with score-based walk-jump sampling for fast all-atom unconditional molecule generation.
Problem
Generating 3D molecules scales poorly with size under point-cloud GNN and voxel-grid representations, limiting expressivity and scalability (e.g., for large macrocyclic peptides).
Approach
Represent each molecule as a continuous atomic occupancy field parameterized by a shared conditional multiplicative filter network with per-molecule latent modulation codes, then perform walk-jump sampling (Langevin walk, single-step denoising jump) in the latent code space and decode codes into atomic coordinates via peak finding and continuous L-BFGS refinement.
Key results
- On GEOM-drugs, FuncMol reaches 69.7% stable molecules and 0.29 s/molecule sampling time, versus VoxMol's 75.0% at 7.55 s/molecule and EDM's 40.3% at 9.35 s/molecule.
- On QM9, FuncMol attains 89.2% stable molecules and 0.05 s/molecule, comparable to VoxMol (89.3%, 0.83 s) and below EDM (97.9%).
- On CREMP macrocyclic peptides, FuncMol generates a molecule in about 1.5 s, while VoxMol could not be trained on this dataset.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace VoxMol with FuncMol's neural-field representation and latent walk-jump generation | 3D molecule generation on GEOM-drugs · GEOM-drugs | sampling time (s/mol): 7.55 -> 0.29 | Helped |
| replace VoxMol with FuncMol | 3D molecule generation · GEOM-drugs | stable mol (%): 75.0 -> 69.7 | Hurt |
| replace VoxMol with FuncMol | 3D molecule generation · GEOM-drugs | QED: .659 -> .713 | Helped |
| replace VoxMol with FuncMol | 3D molecule generation · GEOM-drugs | median strain energy: 69.2 -> 109.7 | Hurt |
| enable continuous coordinate refinement (ablation) | FuncMol molecule decoding · GEOM-drugs | stable mol (%): 78.8 -> 83.1 | Helped |
| enable continuous coordinate refinement (ablation) | FuncMol molecule decoding · QM9 | stable mol (%): 79.1 -> 95.5 | Helped |
| replace walk-jump sampling with diffusion sampling (ablation) | FuncMol_dec · QM9 | stable mol (%): 88.6 -> 70.8 | Hurt |
| replace walk-jump sampling with diffusion sampling (ablation) | FuncMol_dec · GEOM-drugs | molecular stability | Hurt |
| increase walk steps from 1000 to 50000 (ablation) | FuncMol WJS sampling · GEOM-drugs | stable mol (%): 68.8 -> 84.9 | Helped |
| increase walk steps from 1000 to 50000 (ablation) | FuncMol WJS sampling · GEOM-drugs | unique (%): 97.4 -> 66.6 | Hurt |
| decode at 0.167 Å instead of 0.25 Å resolution (ablation) | FuncMol molecule decoding · GEOM-drugs | sampling time (s/mol): .29 -> .89 | Hurt |
| decode at 0.5 Å instead of 0.25 Å resolution (ablation) | FuncMol molecule decoding · GEOM-drugs | stable mol (%): 68.8 -> 58.8 | Hurt |
Surprising findings
- Auto-decoding variant FuncMol_dec memorizes training data, with around 33% of GEOM-drugs generated molecules copied from the training set.
- On QM9, the paper notes that the dataset is not fully suited for unconditional generation, since a perfect model would reproduce training samples due to enumeration.
Limitations
- FuncMol is close to but not uniformly better than VoxMol; it underperforms point-cloud baselines on QM9 stability and atom metrics.
- Sampling bottleneck is atomic coordinate extraction, and the paper notes bonds are not modeled jointly with coordinates.
- Auto-decoding variant is prone to memorization.
Experimental setup
Datasets: QM9 GEOM-drugs CREMP
Benchmarks: QM9 GEOM-drugs CREMP
Metrics: stable molecule % stable atom % validity uniqueness valency W1 atom TV bond TV bond length W1 bond angle W1 sampling time per molecule
Baselines: EDM GeoLDM VoxMol FuncMol-dec diffusion variant
Builds on: walk-jump sampling VoxMol multiplicative filter networks EDM neural empirical Bayes
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