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Equivariant Blurring Diffusion for Hierarchical Molecular Conformer Generation
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Proposes Equivariant Blurring Diffusion (EBD), a coarse-to-fine molecular conformer generator that starts from RDKit fragment-level coordinates and blurs atom positions toward them, using SE(3)-equivariant deblurring networks.
Problem
Generating 3D molecular conformers from molecular graphs in a hierarchical, coarse-to-fine manner, where standard noise-based diffusion corrupts coarse fragment structure as well as fine atomic details.
Approach
Replaces random-noise corruption with a deterministic linear interpolation in Euclidean space from atom coordinates to their RDKit-derived fragment coordinates, and reparameterizes the loss so the network predicts the ground-truth conformer x0 (aligned with Kabsch) rather than the less-blurred previous state.
Key results
- On GEOM-Drugs (delta=1.25 Å), EBD (T=50) reaches COV-R 92.60% mean and MAT-R 0.8216 Å versus GeoDiff (T=5000) at 89.40% and 0.8571 Å.
- On GEOM-Drugs, EBD improves precision with COV-P 66.24% and MAT-P 1.1237 Å versus GeoDiff's 61.28% and 1.1642 Å.
- On GEOM-QM9, EBD attains MAT-P 0.3622 Å versus GeoDiff's 0.4362 Å, though GeoDiff has better MAT-R mean (0.2199 vs 0.2374).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use EBD with T=50 instead of GeoDiff with T=5000 | Molecular conformer generation · Drugs test | COV-R mean (%): 89.40 -> 92.60 | Helped |
| use EBD with T=50 instead of GeoDiff with T=5000 | Molecular conformer generation · Drugs test | COV-P mean (%): 61.28 -> 66.24 | Helped |
| use EBD with T=50 instead of GeoDiff with T=5000 | Molecular conformer generation · QM9 test | MAT-R mean (Å): 0.2199 -> 0.2374 | Hurt |
| use EBD with T=50 instead of GeoDiff with T=5000 | Molecular conformer generation · QM9 test | MAT-P mean (Å): 0.4362 -> 0.3622 | Helped |
| use EBD with T=50 instead of GeoDiff | QM9 conformer generation · QM9 30-molecule subset | mean energy MAE (eV): 0.2597 -> 0.1812 | Helped |
| use RDKit atom conformer prior instead of the fragment prior (ablation) | EBD · Drugs test | COV-P mean (%): 66.24 -> 76.62 | Helped |
| use RDKit atom conformer prior instead of the fragment prior (ablation) | EBD · Drugs test | MAT-R mean (Å): 0.8216 -> 0.7986 | Helped |
| use finer fragments with vocabulary size 50 rather than larger vocabulary sizes (ablation) | EBD · Drugs test | matching scores (MAT-R and MAT-P) | Helped |
| predict the ground-truth state rather than the previous less-blurred state (ablation) | EBD · Drugs test | matching scores (MAT-R and MAT-P) | Helped |
| use linear blurring corruption rather than stochastic random-noise corruption (ablation) | Coarse-to-fine conformer generation · Drugs test | conformer diversity and quality | Helped |
Surprising findings
- Predicting the ground-truth state x0 instead of the previous less-blurred state yields much better conformers, as the earlier estimator produced degenerated conformers with high matching scores.
- EBD with T=50 outperforms GeoDiff with T=5000 on Drugs, using about 100 times fewer diffusion steps.
Limitations
- Sampling needs an extra deterministic blurring step, which can make it slower than the previous-state estimator.
- Discrepancy between ground-truth and RDKit fragment coordinates grows with molecule size, possibly requiring T above 50.
- Uses relatively simple equivariant GNN deblurring networks; more powerful geometric GNNs are left for future work.
Experimental setup
Datasets: GEOM-QM9 GEOM-Drugs
Benchmarks: GEOM-Drugs GEOM-QM9
Metrics: COV-R MAT-R COV-P MAT-P HOMO-LUMO gap MAE energy MAE Wilcoxon signed-rank p-value
Baselines: RDKit CVGAE GraphDG CGCF ConfVAE GeoMol ConfGF GeoDiff DecompDiff
Builds on: Inverse Heat Dissipation Model (IHDM) GeoDiff DecompDiff Principal Subgraph (PS) Kabsch algorithm
Closest papers by meaning
- Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation (ICLR 2024 · similarity 0.91)
- Sampling 3D Molecular Conformers with Diffusion Transformers (NeurIPS 2025 · similarity 0.91)
- Swallowing the Bitter Pill: Simplified Scalable Conformer Generation (ICML 2024 · similarity 0.91)
- Geometric-Facilitated Denoising Diffusion Model for 3D Molecule Generation (AAAI 2024 · similarity 0.90)
- DiSCO: Diffusion Schrödinger Bridge for Molecular Conformer Optimization (AAAI 2024 · similarity 0.90)
- Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment (ICML 2025 · similarity 0.90)
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