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Bridging Geometric States via Geometric Diffusion Bridge
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Proposes Geometric Diffusion Bridge (GDB), an SE(3)-equivariant diffusion bridge built via a modified Doob's h-transform that bridges initial and target geometric states, extended to chains of bridges to exploit trajectory data.
Problem
Predicting the evolution of geometric states (e.g., molecular equilibrium conformations, catalyst adsorption states) from initial states while preserving joint state distributions, respecting SE(3) symmetry, and leveraging trajectory data.
Approach
Construct an SE(3)-equivariant diffusion bridge anchored at initial and target geometric states via an equivariant Doob's h-transform with Gaussian kernels, and chain such bridges to model trajectories; train with a simulation-free matching objective and sample with probability-flow ODE solvers.
Key results
- On QM9, GDB reaches 0.148 Å test C-RMSD versus 0.367 for the best baseline GTMGC (about 59.7% relative reduction).
- On OC22 IS2RS validation, GDB achieves 59.39% average ADwT versus 57.42% for GemNet-OC trained on OC20+OC22 (about 3.4% relative gain).
- Ablating the R^0 condition drops OC22 average ADwT from 59.39 to 54.71.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GDB instead of GTMGC | Equilibrium state prediction · QM9 test | C-RMSD: 0.367 -> 0.148 | Helped |
| Use GDB instead of GTMGC | Equilibrium state prediction · Molecule3D random split test | C-RMSD: 0.713 -> 0.619 | Helped |
| Use GDB instead of GTMGC | Equilibrium state prediction · Molecule3D scaffold split test | C-RMSD: 0.693 -> 0.603 | Helped |
| Use GDB instead of GemNet-OC trained on OC20+OC22 | OC22 IS2RS structure relaxation · OC22 IS2RS validation | ADwT: 57.42 -> 59.39 | Helped |
| Add trajectory guidance (ablation) | GDB · OC22 IS2RS validation | ADwT: 58.54 -> 59.39 | Helped |
| Add trajectory guidance (ablation) | GDB · OC22 IS2RS validation OOD | ADwT: 54.94 -> 55.78 | Helped |
| Add initial-state condition (ablation) | GDB · OC22 IS2RS validation | ADwT: 54.71 -> 59.39 | Helped |
| Add initial-state condition (ablation) | GDB · OC22 IS2RS validation OOD | ADwT: 49.26 -> 55.78 | Helped |
Surprising findings
- Without trajectory guidance, GDB still outperforms GemNet-OC trained on 10x more data (58.54 vs 57.42 average ADwT).
Limitations
- Advanced training objectives and sampling algorithms were not explored for generality.
- Transformer-based architectures may limit efficiency.
Experimental setup
Datasets: QM9 Molecule3D OC22 OC20
Benchmarks: QM9 Molecule3D OC22 IS2RS
Metrics: D-MAE D-RMSE C-RMSD ADwT
Baselines: RDKit DG RDKit ETKDG GINE GATv2 GPS GTMGC DeeperGCN-DAGNN SpinConv GemNet-OC GemNet-dT GemNet-OC-Large
Builds on: Doob's h-transform denoising score matching GemNet-OC Graph Transformer equivariant network
Closest papers by meaning
- Geometric Trajectory Diffusion Models (NeurIPS 2024 · similarity 0.91)
- Geometric-Facilitated Denoising Diffusion Model for 3D Molecule Generation (AAAI 2024 · similarity 0.88)
- GeoAda: Efficiently Finetune Geometric Diffusion Models with Equivariant Adapters (NeurIPS 2025 · similarity 0.88)
- Vector Field Oriented Diffusion Model for Crystal Material Generation (AAAI 2024 · similarity 0.87)
- Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation (ICLR 2024 · similarity 0.86)
- Enhancing Generalizability in Molecular Conformation Generation with METRIZATION-Informed Geometric Diffusion Pretraining (AAAI 2025 · similarity 0.86)
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