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DiSCO: Diffusion Schrödinger Bridge for Molecular Conformer Optimization
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Proposes DiSCO, an SE(3)-equivariant tractable Schrödinger bridge that refines conformers from any existing generator toward the ground-truth (CREST) conformer distribution, improving ensemble RMSD and property prediction.
Problem
Conformer generators approximate the low-energy conformational landscape imperfectly, leaving a gap between generated conformers and the ground-truth Boltzmann-like distribution; direct Euclidean generation has a vast search space and needs SE(3) equivariance.
Approach
Builds a tractable diffusion Schrödinger bridge (adapted from I2SB) between the ground-truth conformer distribution and the output distribution of any existing generator, trained with SE(3)-equivariant networks and Kabsch alignment, so it works as a model-agnostic post hoc refinement step.
Key results
- On GEOM-Drugs, Torsional Diffusion + DiSCO raises mean COV-P from 80.00% to 82.73% and lowers mean MAT-P from 0.9221 to 0.8688 Å.
- RDKit ETKDG + DiSCO raises mean COV-R from 59.45% to 77.22% and mean COV-P from 72.06% to 77.17%.
- Energy MAE with xTB drops from 1.27 to 0.79 kcal/mol for RDKit ETKDG and from 1.09 to 0.85 for Torsional Diffusion after DiSCO.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Optimize Torsional Diffusion conformers with DiSCO | Torsional Diffusion · GEOM-Drugs | COV-R (mean, %): 93.71 -> 95.31 | Helped |
| Optimize Torsional Diffusion conformers with DiSCO | Torsional Diffusion · GEOM-Drugs | MAT-R (mean, Å): 0.7008 -> 0.6496 | Helped |
| Optimize Torsional Diffusion conformers with DiSCO | Torsional Diffusion · GEOM-Drugs | COV-P (mean, %): 80.00 -> 82.73 | Helped |
| Optimize Torsional Diffusion conformers with DiSCO | Torsional Diffusion · GEOM-Drugs | MAT-P (mean, Å): 0.9221 -> 0.8688 | Helped |
| Optimize DMCG conformers with DiSCO | DMCG · GEOM-Drugs | COV-R (mean, %): 96.76 -> 96.10 | Hurt |
| Optimize DMCG conformers with DiSCO | DMCG · GEOM-Drugs | MAT-R (mean, Å): 0.7183 -> 0.7119 | Helped |
| Optimize DMCG conformers with DiSCO | DMCG · GEOM-Drugs | COV-P (mean, %): 79.37 -> 83.31 | Helped |
| Optimize RDKit + Clustering conformers with DiSCO | RDKit + Clustering · GEOM-Drugs | COV-R (mean, %): 88.13 -> 94.89 | Helped |
| Optimize RDKit + Clustering conformers with DiSCO | RDKit + Clustering · GEOM-Drugs | COV-P (mean, %): 69.46 -> 76.56 | Helped |
| Optimize RDKit ETKDG conformers with DiSCO | RDKit ETKDG · GEOM-QM9 | E: 1.27 -> 0.79 | Helped |
| Optimize Torsional Diffusion conformers with DiSCO | Torsional Diffusion · GEOM-QM9 | Emin: 1.40 -> 0.33 | Helped |
| Optimize RDKit ETKDG conformers with DiSCO | RDKit ETKDG · GEOM-QM9 | ∆ϵ: 1.37 -> 1.38 | Hurt |
Surprising findings
- DiSCO slightly lowers mean COV-R for Torsional Diffusion-generated... actually the mean COV-R for DMCG and RDKit+Clustering-related variants is not uniformly improved, so the method does not achieve best mean COV-R across all settings.
Limitations
- Assumes independence between the generated conformer C1 and ground-truth conformer C0 rather than modeling the conditional distribution.
- Mean COV-R does not always improve after DiSCO (e.g., DMCG and Torsional Diffusion show slight decreases), and the paper states state-of-the-art except for mean COV-R.
Experimental setup
Datasets: GEOM-QM9 GEOM-Drugs
Benchmarks: GEOM-Drugs GEOM-QM9
Metrics: COV-R MAT-R COV-P MAT-P MAE of xTB energy, HOMO-LUMO gap
Baselines: RDKit ETKDG Torsional Diffusion DMCG RDKit + Clustering CONFVAE CONFGF GEODIFF
Builds on: I2SB (image-to-image Schrödinger bridge) DDPM GeoDiff Torsional Diffusion
Closest papers by meaning
- Swallowing the Bitter Pill: Simplified Scalable Conformer Generation (ICML 2024 · similarity 0.91)
- Equivariant Blurring Diffusion for Hierarchical Molecular Conformer Generation (NeurIPS 2024 · similarity 0.90)
- Enhancing Generalizability in Molecular Conformation Generation with METRIZATION-Informed Geometric Diffusion Pretraining (AAAI 2025 · similarity 0.89)
- WGFormer: An SE(3)-Transformer Driven by Wasserstein Gradient Flows for Molecular Ground-State Conformation Prediction (ICML 2025 · similarity 0.89)
- Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation (ICLR 2024 · similarity 0.89)
- Efficient Molecular Conformer Generation with SO(3)-Averaged Flow Matching and Reflow (ICML 2025 · similarity 0.89)
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