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Unifying Generation and Prediction on Graphs with Latent Graph Diffusion
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Proposes Latent Graph Diffusion (LGD), which formulates regression and classification as conditional latent diffusion generation so one graph diffusion model handles generation and prediction at node, edge and graph levels.
Problem
Graph generative models cannot address regression or classification, and existing graph diffusion models fail to generate structure and features simultaneously across all levels and feature types.
Approach
Encode graphs (with augmented no-edge types) into a continuous latent space using a pretrained graph transformer encoder, train a DDPM-style diffusion model there with an augmented-edge graph transformer and cross-attention conditioning, and cast regression/classification as conditional generation of labels given a partially masked graph.
Key results
- On ZINC12k regression, LGD-DDPM reaches 0.065 MAE, beating GPS (0.070) and other baselines.
- On node classification, LGD reports 96.94% on Photo, 98.55% on Physics and 73.17% on OGBN-Arxiv, best among listed methods.
- Unconditional QM9 generation: LGD-large attains the best FCD (0.10) and NSPDK (0.0002) among compared models, with validity 99.13%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use LGD-large for unconditional molecule generation | QM9 molecule generation · QM9 | FCD: 0.11 -> 0.10 | Helped |
| use LGD-large for unconditional molecule generation | QM9 molecule generation · QM9 | Validity (%): 99.69 -> 99.13 | Hurt |
| use LGD for conditional molecule generation | QM9 conditional generation · QM9 | MAE (μ): 1.108 -> 0.879 | Helped |
| use LGD for conditional molecule generation | QM9 conditional generation · QM9 | MAE (α): 2.37 -> 2.43 | Hurt |
| use LGD for conditional molecule generation | QM9 conditional generation · QM9 | MAE (εHOMO): 340 -> 313 | Helped |
| use LGD for conditional molecule generation | QM9 conditional generation · QM9 | MAE (εLUMO): 522 -> 641 | Hurt |
| use LGD for conditional molecule generation | QM9 conditional generation · QM9 | MAE (Δε): 587 -> 586 | Helped |
| use LGD for conditional molecule generation | QM9 conditional generation · QM9 | MAE (cv): 1.025 -> 1.002 | Helped |
| use LGD-DDPM instead of GPS | ZINC12K molecular property regression · ZINC12K test | MAE: 0.070±0.004 -> 0.065± 0.003 | Helped |
| use DDIM inference instead of DDPM (ablation) | LGD on ZINC12K · ZINC12K test | MAE: 0.065± 0.003 -> 0.081± 0.006 | Hurt |
| use LGD for node classification | Photo node classification · Photo | accuracy: 95.49 ± 0.11 -> 96.94±0.14 | Helped |
| use LGD for node classification | Physics node classification · Physics | accuracy: 97.34 ± 0.03 -> 98.55± 0.12 | Helped |
Surprising findings
- Generative regression with LGD outperforms deterministic graph transformers on ZINC12k despite single-sample predictions.
- LGD has lower novelty than most baselines (e.g., 38.56% vs 86% for GDSS on QM9).
Limitations
- Models are trained separately per task rather than as a single foundation model.
- Only validated on graph tasks; applicability to other domains such as computer vision is untested.
Experimental setup
Datasets: QM9 ZINC12k Amazon Photo Coauthor Physics OGBN-Arxiv MOSES
Benchmarks: QM9 ZINC12k Amazon Photo Coauthor Physics OGBN-Arxiv
Metrics: validity uniqueness FCD NSPDK novelty MAE accuracy
Baselines: MoFlow GraphAF GraphDF GDSS DiGress HGGT GruM EDM GeoLDM GIN PNA GPS
Builds on: DDPM DDIM Stable Diffusion GRIT EGT GraphGPS
Closest papers by meaning
- SBGD: Improving Graph Diffusion Generative Model via Stochastic Block Diffusion (ICML 2025 · similarity 0.91)
- Generating Graphs via Spectral Diffusion (ICLR 2025 · similarity 0.89)
- Graph Generation with Diffusion Mixture (ICML 2024 · similarity 0.89)
- When Edge Independence Fails: Joint Graph Diffusion with Latent Sociability Priors (NeurIPS 2026 · similarity 0.89)
- SDMG: Smoothing Your Diffusion Models for Powerful Graph Representation Learning (ICML 2025 · similarity 0.89)
- Efficient and Scalable Graph Generation through Iterative Local Expansion (ICLR 2024 · similarity 0.88)
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