A Group Symmetric Stochastic Differential Equation Model for Molecule Multi-modal Pretraining
Abstract
Molecule pretraining has quickly become the go-to schema to boost the performance of AI-based drug discovery. Naturally, molecules can be represented as 2D topological graphs or 3D geometric point clouds. Although most existing pertaining methods focus on merely the single modality, recent research has shown that maximizing the mutual information (MI) between such two modalities enhances the molecule representation ability. Meanwhile, existing molecule multi-modal pretraining approaches approximate MI based on the representation space encoded from the topology and geometry, thus resulting in the loss of critical structural information of molecules. To address this issue, we propose MoleculeSDE. MoleculeSDE leverages group symmetric (e.g., SE(3)-equivariant and reflection-antisymmetric) stochastic differential equation models to generate the 3D geometries from 2D topologies, and vice versa, directly in the input space. It not only obtains tighter MI bound but also enables prosperous downstream tasks than the previous work. By comparing with 17 pretraining baselines, we empirically verify that MoleculeSDE can learn an expressive representation with state-of-the-art performance on 26 out of 32 downstream tasks.
Benchmark Results
Tested on 7 datasets 17 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
MoleculeNet
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | HIMP | 0.8740
±0.0050 | |
| 2 | GINE w/ VN | 0.8720
±0.0030 | |
| 3 | NaiveGINe+ K=3 w/ VN | 0.8700
±0.0040 | |
| 14 | GCN | 0.8400
±0.0040 | |
| 46 | ContextPred | 0.8060
±0.0120 best reported | best at pub: KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Prediction (KDD 2022) |
| 48 | 3D Infomax | 0.8050
±0.0320 best reported | best at pub: KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Prediction (KDD 2022) Difference within reported uncertainty; not counted as underperformance. |
| 61 | GraphMVP | 0.7990
±0.0180 best reported | best at pub: KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Prediction (KDD 2022) |
| 67 | MolCLR | 0.7980
±0.0070 best reported | |
| 81 | InfoGraph | 0.7930 best reported | best at pub: GeomGCL: Geometric Graph Contrastive Learning for Molecular Property Prediction (AAAI 2021) |
| 161 | MoleculeSDE | 0.7680
±0.0034 | This paper |
| 197 | SDE (MoleculeSDE) | 0.7560 | This paper |
| 216 | -- (random init) | 0.7530
±0.0022 | This paper |
| 229 | AttrMask | 0.7480
±0.0025 | prev best: 16 Pre-training Molecular Graph Representation with 3D Geometry (ICLR 2021) Improvement within reported uncertainty; not highlighted. |
| 270 | VRR (GraphMVP) | 0.7360 | This paper |
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | ProtoMol | 0.9140
±0.0030 | |
| 2 | MMSG | 0.9080
±0.0050 | |
| 3 | MemGNN | 0.9070 | |
| 9 | MolCLR | 0.8900
±0.0030 best reported | |
| 43 | GIN | 0.8646
±0.0081 best reported | best at pub: Optimal Transport Graph Neural Networks (2020) |
| 64 | GCN | 0.8540
±0.0110 | |
| 149 | GraphMVP | 0.8120
±0.0090 best reported | best at pub: Unified 2D and 3D Pre-Training of Molecular Representations (KDD 2022) best today: Invariant-Based Diagnostics for Graph Benchmarks (2026) Difference within reported uncertainty; not counted as underperformance. |
| 170 | MoleculeSDE | 0.8040
±0.0092 | This paper |
| 182 | AttrMask | 0.7970
±0.0033 | prev best: 16 Pre-training Molecular Graph Representation with 3D Geometry (ICLR 2021) Improvement within reported uncertainty; not highlighted. |
| 183 | 3D Infomax | 0.7970
±0.0154 | This paper |
| 186 | ContextPred | 0.7960
±0.0120 best reported | best at pub: 16 Pre-training Molecular Graph Representation with 3D Geometry (ICLR 2021) best today: Dual-perspective Cross Contrastive Learning in Graph Transformers (2024) Difference within reported uncertainty; not counted as underperformance. |
| 204 | InfoGraph | 0.7890
±0.0110 best reported | best at pub: Omni-Granular Ego-Semantic Propagation for Self-Supervised Graph Representation Learning (ICML 2022) Difference within reported uncertainty; not counted as underperformance. |
| 209 | SchNet (MoleculeSDE) | 0.7860
±0.0040 | This paper |
| 237 | -- (random init) | 0.7670
±0.0251 | This paper |
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | MAGPrompt+ | 0.9432
±0.0238 | |
| 2 | CamS-LLaMA | 0.9420 | |
| 3 | SE(3)-I MPPH | 0.9400
±0.0210 | |
| 34 | GIN | 0.8875
±0.0049 | |
| 40 | ContextPred | 0.8770
±0.0260 best reported | best at pub: KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Prediction (KDD 2022) |
| 41 | 3D Infomax | 0.8770
±0.0140 best reported | best at pub: KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Prediction (KDD 2022) |
| 49 | GraphMVP | 0.8600
±0.0340 best reported | best at pub: KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Prediction (KDD 2022) |
| 78 | MolCLR | 0.7360
±0.0050 best reported | |
| 80 | MoleculeSDE | 0.7320
±0.0048 | This paper |
| 141 | AttrMask | 0.7020
±0.0050 best reported | best at pub: 16 Pre-training Molecular Graph Representation with 3D Geometry (ICLR 2021) best today: Graph Generative Pre-trained Transformer (ICML 2025) Difference within reported uncertainty; not counted as underperformance. |
| 173 | InfoGraph | 0.6920
±0.0080 best reported | best at pub: 16 Pre-training Molecular Graph Representation with 3D Geometry (ICLR 2021) best today: Graph Generative Pre-trained Transformer (ICML 2025) |
| 200 | random init | 0.6810
±0.0059 | This paper |
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | SE(3)-I MPPH | 0.9930
±0.0040 | |
| 2 | KA-GCN | 0.9920
±0.0050 | |
| 3 | KA-GAT | 0.9910
±0.0050 | |
| 12 | MolCLR | 0.9320
±0.0170 best reported | |
| 19 | GCN | 0.9130
±0.0170 | |
| 40 | AttrMask | 0.8770
±0.0119 | prev best: 16 Pre-training Molecular Graph Representation with 3D Geometry (ICLR 2021) Improvement within reported uncertainty; not highlighted. |
| 46 | MoleculeSDE | 0.8700
±0.0053 | This paper |
| 49 | GraphMVP | 0.8650
±0.0170 | prev best: 16 Pre-training Molecular Graph Representation with 3D Geometry (ICLR 2021) |
| 89 | 3D Infomax | 0.7990
±0.0349 | This paper |
| 106 | InfoGraph | 0.7810 best reported | best at pub: GeomGCL: Geometric Graph Contrastive Learning for Molecular Property Prediction (AAAI 2021) Difference within reported uncertainty; not counted as underperformance. |
| 115 | ContextPred | 0.7720
±0.0088 | prev best: 16 Pre-training Molecular Graph Representation with 3D Geometry (ICLR 2021) Improvement within reported uncertainty; not highlighted. |
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | KA-GAT | 0.8470
±0.0020 | |
| 2 | KA-GCN | 0.8420
±0.0010 | |
| 3 | GraphKAN | 0.8370
±0.0010 | |
| 14 | MolCLR | 0.6800
±0.0110 best reported | |
| 66 | GIN | 0.6403
±0.0104 best reported | |
| 70 | GraphMVP | 0.6390
±0.0120 best reported | best at pub: Unified 2D and 3D Pre-Training of Molecular Representations (KDD 2022) |
| 103 | ContextPred | 0.6220
±0.0059 | prev best: KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Prediction (KDD 2022) Improvement within reported uncertainty; not highlighted. |
| 125 | GCN | 0.6150
±0.0250 | |
| 134 | AttrMask | 0.6120
±0.0012 | prev best: 16 Pre-training Molecular Graph Representation with 3D Geometry (ICLR 2021) Improvement within reported uncertainty; not highlighted. |
| 148 | MoleculeSDE | 0.6080
±0.0039 | This paper |
| 155 | 3D Infomax | 0.6060
±0.0078 | prev best: KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Prediction (KDD 2022) Improvement within reported uncertainty; not highlighted. |
| 162 | InfoGraph | 0.5990
±0.0030 | prev best: Omni-Granular Ego-Semantic Propagation for Self-Supervised Graph Representation Learning (ICML 2022) Improvement within reported uncertainty; not highlighted. |
| 165 | SchNet with MoleculeSDE | 0.6050
±0.0039 | This paper |
| 179 | SchNet with ConfGF | 0.6010
±0.0087 | This paper |
| 196 | SchNet with MMFF | 0.5940
±0.0027 | This paper |
| 230 | SchNet with ClofNet | 0.5600
±0.0010 | This paper |
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | GeomGCL | 0.7630 | |
| 2 | LiGhT DeepGPT | 0.7570
±0.0110 | |
| 3 | CoMPT | 0.7550 | |
| 14 | GCN | 0.7350
±0.0020 | |
| 25 | 3D Infomax | 0.7160
±0.0130 best reported | best at pub: KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Prediction (KDD 2022) |
| 28 | ContextPred | 0.7140
±0.0180 best reported | best at pub: KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Prediction (KDD 2022) |
| 35 | InfoGraph | 0.7050 best reported | best at pub: GeomGCL: Geometric Graph Contrastive Learning for Molecular Property Prediction (AAAI 2021) |
| 50 | GraphMVP | 0.6890
±0.0100 best reported | best at pub: KPGT: Knowledge-Guided Pre-training of Graph Transformer for Molecular Property Prediction (KDD 2022) |
| 103 | MoleculeSDE | 0.6520
±0.0031 | This paper |
| 150 | AttrMask | 0.6290
±0.0011 | prev best: 16 Pre-training Molecular Graph Representation with 3D Geometry (ICLR 2021) Improvement within reported uncertainty; not highlighted. |
| 166 | MolCLR | 0.6290
±0.0038 | This paper |
Quantum Chemistry
| # | Model | MAE ↓ | Paper |
|---|---|---|---|
| 1 | QHNet | 0.0000 | |
| 2 | QHNetV2 | 0.0000 | |
| 3 | PhiSNet | 0.0000 | |
| 104 | MoleculeSDE | 0.2820 best reported | |
| 108 | random init | 0.3800 | This paper |
