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Lift Your Molecules: Molecular Graph Generation in Latent Euclidean Space
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Maps 2D molecular graphs to latent 3D point clouds via synthetic conformer coordinates (SyCo) and trains an EDM on that latent space, yielding an all-at-once atom-based molecular graph generator (EDM-SyCo) with inpainting+guidance for similarity-constrained optimization.
Problem
Molecular graph generation is hard due to discrete, sparse graph structure; existing VAE-based autoregressive methods use fixed-size latents and generation orders, while discrete diffusion (DiGress) struggles with joint node/edge distributions and optimization.
Approach
Encode molecular graphs as latent Euclidean point clouds using RDKit ETKDG synthetic conformers plus an EGNN encoder, decode with node/edge MLP classifiers, and then reuse a pretrained 3D point-cloud diffusion model (EDM) on this latent space; add a similarity-constrained optimization that combines RePaint-style inpainting (to add atoms) with regressor guidance.
Key results
- EDM-SyCo reaches FCD 0.85 on ZINC250K (best overall), outperforming DiGress (0.65) by about 30%.
- On GuacaMol, EDM-SyCo achieves FCD 0.79 vs DiGress 0.68 (about 16% gain).
- Property-conditional MW MAE of 3.86 vs DiGress 60.30 and FreeGress 15.18; similarity-constrained LogP optimization improvement 3.11 vs best optimization baseline GCPN 2.49.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use SyCo latent point clouds with EDM instead of direct discrete graph diffusion | molecular graph generation · ZINC250K | FCD: 0.65 -> 0.85 | Helped |
| use SyCo latent point clouds with EDM instead of direct discrete graph diffusion | molecular graph generation · GuacaMol | FCD: 0.68 -> 0.79 | Helped |
| use continuous latent-space regressor guidance instead of discrete guidance | conditional LogP generation · LogP conditional generation | MAE: 0.49 -> 0.18 | Helped |
| use continuous latent-space regressor guidance instead of discrete guidance | conditional molecular-weight generation · Molecular weight conditional generation | MAE: 60.30 -> 3.86 | Helped |
| use EDM-SyCo instead of FreeGress | conditional generation · LogP conditional generation | MAE: 0.15 -> 0.18 | Mixed |
| use EDM-SyCo instead of FreeGress | conditional generation · Molecular weight conditional generation | MAE: 15.18 -> 3.86 | Helped |
| use EDM-SyCo instead of GCPN | similarity-constrained optimization · LogP similarity optimization (sim ≥ 0.4) | improvement: 2.49 -> 3.11 | Helped |
| use EDM-SyCo instead of GCPN | similarity-constrained optimization · QED similarity optimization (sim ≥ 0.4) | success rate: 9.4% -> 46.4% | Helped |
| include an EGNN encoder rather than the MLP-only variant (ablation) | SyCo autoencoder · ZINC250K graph reconstruction | accuracy: 11.77% -> 99.93% | Helped |
| use a learned EGNN + MLP autoencoder rather than a rule-based system (ablation) | SyCo autoencoder · ZINC250K graph reconstruction | accuracy: 11.78% -> 99.93% | Helped |
| train the autoencoder and diffusion model in two stages rather than jointly (ablation) | EDM-SyCo · molecular generation | generation performance | Helped |
Limitations
- Number of atoms must be fixed in advance for diffusion sampling; variable-size generation left for future work.
- Optimization cannot remove atoms; decoder often predicts disconnected subgraphs.
- High inference cost inherited from diffusion models.
Experimental setup
Datasets: ZINC250K GuacaMol
Benchmarks: ZINC250K GuacaMol
Metrics: FCD KL divergence MAE validity Tanimoto similarity improvement success rate diversity
Baselines: GraphAF PS-VAE HierVAE MiCaM JT-VAE MAGNet MoLeR DiGress FreeGress CGVAE Seq2Seq AtomG2G
Builds on: EDM EGNN RePaint GeoLDM DiGress
Closest papers by meaning
- Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment (ICML 2025 · similarity 0.89)
- Learning Disentangled Equivariant Representation for Explicitly Controllable 3D Molecule Generation (AAAI 2025 · similarity 0.89)
- Equivariant Neural Diffusion for Molecule Generation (NeurIPS 2024 · similarity 0.88)
- Geometric-Facilitated Denoising Diffusion Model for 3D Molecule Generation (AAAI 2024 · similarity 0.88)
- NEAT: Neighborhood-Guided, Efficient, Autoregressive Set Transformer for 3D Molecular Generation (NeurIPS 2026 · similarity 0.88)
- Towards Unified and Lossless Latent Space for 3D Molecular Latent Diffusion Modeling (NeurIPS 2025 · similarity 0.88)
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