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Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment
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Proposes RADM, which learns a sample-dependent SO(3) rotation per molecule via an autoencoder to build a rotationally aligned latent space, then trains a non-equivariant (GNN or DiT) latent diffusion model for 3D molecule generation.
Problem
Equivariant diffusion models (EDM, GeoLDM) dominate 3D molecule generation but their specialized SE(3)-equivariant architectures limit scalability and efficiency; non-equivariant diffusion models have performed much worse.
Approach
Learn a sample-dependent SO(3) alignment for each molecule through a jointly trained non-equivariant autoencoder (rotation predicted by a GNN and parameterized via SVD projection), so that the latent space is aligned and a plain non-equivariant denoiser (GNN or DiT) can model the distribution well.
Key results
- On QM9, RADM DiT-B reaches 98.5% atom stability, 87.3% molecule stability and 94.1% validity, versus GeoLDM's 98.9%, 89.4% and 93.8%, and far above non-equivariant GraphLDM-aug (97.9%, 78.7%, 90.5%).
- On GEOM-Drugs, RADM DiT-B reaches 85.0% atom stability and 99.3% validity, outperforming GeoLDM's 84.4% atom stability at equal validity.
- RADM DiT-S sampling takes 7s per 100 samples versus 49s for GeoLDM and 55s for EDM on a single RTX 4090 (1000 sampling steps).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use learned rotational alignment with the RADM GNN diffusion model instead of PCA alignment (ablation) | RADM GNN · QM9 | molecule stability: 81.9 -> 85.8 | Helped |
| Use learned rotational alignment with the RADM GNN diffusion model instead of PCA alignment (ablation) | RADM GNN · QM9 | validity: 91.7 -> 93.8 | Helped |
| Use learned rotational alignment instead of no learned alignment (ablation) | RADM GNN · QM9 | molecule stability: 70.5 -> 85.8 | Helped |
| Use learned rotational alignment instead of no learned alignment (ablation) | RADM GNN · QM9 | validity: 90.5 -> 93.8 | Helped |
| Scale the diffusion backbone from DiT-S to DiT-B (ablation) | RADM · QM9 | molecule stability: 83.4$\pm$0.2 -> 87.3$\pm$0.2 | Helped |
| Scale the diffusion backbone from DiT-S to DiT-B (ablation) | RADM · GEOM-Drugs | atom stability: 83.8 -> 85.0 | Helped |
| Use RADM DiT-B instead of GeoLDM | RADM DiT-B · QM9 | validity: 93.8 -> 94.1 | Helped |
| Use RADM DiT-B instead of GeoLDM | RADM DiT-B · QM9 | molecule stability: 89.4 -> 87.3$\pm$0.2 | Hurt |
| Use RADM DiT-B instead of GeoLDM | RADM DiT-B · GEOM-Drugs | validity: 99.3 -> 99.3 | No clear effect |
| Use RADM DiT-B instead of GeoLDM | RADM DiT-B · GEOM-Drugs | atom stability: 84.4 -> 85.0 | Helped |
| Use RADM DiT-S instead of EDM | RADM DiT-S · QM9 | molecule stability: 82.0 -> 83.4$\pm$0.2 | Helped |
| Use RADM DiT-S instead of EDM-bridge | RADM DiT-S · QM9 | validity: 92.0 -> 92.5$\pm$0.3 | Helped |
Surprising findings
- RADM with a plain GNN denoiser (RADM_GNN) outperforms RADM with DiT-S on QM9, which the authors attribute to the GNN's global receptive field and more gradient updates from a smaller batch size.
- A non-equivariant decoder is necessary: with equivariant encoder and decoder the L2 reconstruction loss is rotation-invariant, so the rotation network gets no supervision signal.
Limitations
- Hyperparameters largely follow the equivariant baselines (GeoLDM, EDM) and were not tuned for the non-equivariant model.
- Molecule stability on QM9 remains slightly below GeoLDM (87.3% vs 89.4%).
- Relies on a two-stage pipeline with separately trained autoencoder and diffusion model; scale of experiments limited to QM9 and GEOM-Drugs.
Experimental setup
Datasets: QM9 GEOM-Drugs
Benchmarks: QM9 GEOM-Drugs
Metrics: atom stability molecule stability validity validity x uniqueness MAE of property predictor training time per epoch sampling time per 100 samples parameter count
Baselines: EDM EDM-bridge GeoLDM GDM GDM-aug GraphLDM GraphLDM-aug ENF G-SchNet
Builds on: EDM GeoLDM DiT EGNN DDPM
Closest papers by meaning
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