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Efficient Molecular Conformer Generation with SO(3)-Averaged Flow Matching and Reflow
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Proposes SO(3)-Averaged Flow, a closed-form rotation-averaged flow-matching objective, plus reflow and distillation, to enable fast training and one-step molecular conformer generation on GEOM-QM9 and GEOM-Drugs.
Problem
Molecular conformer generation with flow/diffusion models is computationally expensive to train and slow to sample, and prior flow models need rotational alignment (Kabsch) of noise and data.
Approach
Analytically integrate out SO(3) rotations of the conformer data in the conditional flow-matching target, yielding an averaged probability flow that avoids rotational alignment; then straighten trajectories with reflow and distill into one-step generators.
Key results
- AvgFlow-DiT-1step (52M) reaches 76.8% COV-R and 61.0% COV-P mean on GEOM-Drugs, outperforming two-step ET-Flow on recall and MCF variants on precision.
- AvgFlow-NequIP achieves 96.4% COV-R on GEOM-QM9 (best), and AvgFlow-DiT 95.0% COV-P with lowest AMR-P (0.088 A).
- AvgFlow-NequIP two-step generation takes 2.68 ms per conformer on GEOM-Drugs, 21 to 50x faster than MCF DDIM 3-step variants.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace conditional OT or Kabsch alignment with SO(3)-Averaged Flow training | NequIP and DiT flow-matching models · GEOM-Drugs, 300-molecule training-convergence subset | COV-P and AMR-P: AvgFlow NequIP: COV-P 50.9% vs Kabsch 50.5%; AMR-P 0.814 Å vs 0.815 Å | Helped |
| replace conditional OT with SO(3)-Averaged Flow training | NequIP flow-matching model · GEOM-Drugs, 300-molecule training-convergence subset | COV-P: 49.1% -> 49.3% | Helped |
| replace Kabsch alignment with SO(3)-Averaged Flow training | DiT flow-matching model · GEOM-Drugs, 300-molecule training-convergence subset | all four conformer metrics | Helped |
| replace conditional OT with SO(3)-Averaged Flow training | DiT flow-matching model · GEOM-Drugs, 300-molecule training-convergence subset | precision metrics | Helped |
| add reflow to straighten trajectories (ablation) | AvgFlow NequIP · GEOM-Drugs, fewer than 5 ODE steps | COV-R and COV-P: without reflow, 0% coverage at 1 step | Helped |
| add distillation after reflow (ablation) | AvgFlow NequIP · GEOM-Drugs, 1-step generation | COV-R, COV-P, and RMSD | Helped |
| use 1-step instead of 2-step sampling after reflow and distillation (ablation) | AvgFlow NequIP · GEOM-QM9 test | COV-R mean (%): 95.9 -> 95.1 | Hurt |
| use 1-step instead of 2-step sampling after reflow and distillation (ablation) | AvgFlow NequIP · GEOM-QM9 test | AMR-R mean (Å): 0.151 -> 0.220 | Hurt |
Surprising findings
- Averaged Flow NequIP collapses to 0% coverage at one ODE step without reflow, while reflow+distillation recovers one-step quality.
- Reflow reduces precision metrics relative to the base model, a trade-off noted by the authors.
Limitations
- Averaged Flow with many conformers scales linearly in cost with number of conformers (73.5 ms at 1000 conformers per batch of 1000 graphs).
- One-step and two-step precision metrics lag behind full-simulation models, and reflow reduces precision.
- Chirality correction is a post-hoc step with RDKit.
Experimental setup
Datasets: GEOM-QM9 GEOM-Drugs
Benchmarks: GEOM-QM9 GEOM-Drugs
Metrics: COV-R AMR-R COV-P AMR-P wall-clock sampling time
Baselines: RDKit OMEGA GeoMol Torsional Diffusion ET-Flow MCF Conditional OT Kabsch alignment
Builds on: Flow Matching Rectified flow Torsional diffusion NequIP Diffusion Transformer
Closest papers by meaning
- Swallowing the Bitter Pill: Simplified Scalable Conformer Generation (ICML 2024 · similarity 0.90)
- Enhancing Generalizability in Molecular Conformation Generation with METRIZATION-Informed Geometric Diffusion Pretraining (AAAI 2025 · similarity 0.89)
- Energy-Based Flow Matching for Generating 3D Molecular Structure (ICML 2025 · similarity 0.89)
- DiSCO: Diffusion Schrödinger Bridge for Molecular Conformer Optimization (AAAI 2024 · similarity 0.89)
- ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generation (NeurIPS 2024 · similarity 0.89)
- FlashMol: High-Quality Molecule Generation in as Few as Four Steps (NeurIPS 2026 · similarity 0.88)
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