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GLAD: Improving Latent Graph Generative Modeling with Simple Quantization
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GLAD learns a graph generative model in a permutation-equivariant discrete latent space (finite scalar quantization of node embeddings) using diffusion bridges with a closed-form prior-matching objective.
Problem
Latent-space graph generative models have lagged behind data-space models; continuous latent spaces suffer from latent-node collapse and poor reconstruction, and discrete/autoregressive alternatives are not permutation-invariant.
Approach
Quantize equivariant GNN node embeddings per dimension (finite scalar quantization) to form a discrete latent node grid, then adapt diffusion bridges for constrained discrete domains to learn the latent graph prior with a permutation-equivariant graph transformer drift model.
Key results
- On QM9, GLAD reaches FCD 0.201 and NSPDK 0.0003, the best among compared methods, with validity 97.12%.
- On ZINC250k, GLAD achieves FCD 2.54 and NSPDK 0.002, improving over the next best DGAE (FCD 4.4, NSPDK 0.007).
- On generic graphs, GLAD has the lowest average MMD on Community-small (0.028), Ego-small (0.010), and Enzymes (0.009).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use quantized rather than unquantized latent nodes (ablation) | GLAD · QM9 | FCD: 1.207 -> 0.201 | Helped |
| use quantized rather than unquantized latent nodes (ablation) | GLAD · QM9 | NSPDK: 0.0009 -> 0.0003 | Helped |
| use quantized rather than unquantized latent nodes (ablation) | GLAD · QM9 | Val.: 83.12 -> 97.12 | Helped |
| replace the fixed zero prior with a standard normal prior (ablation) | GLAD · QM9 | FCD: 0.201 -> 0.330 | Hurt |
| replace the fixed zero prior with a standard normal prior (ablation) | GLAD · QM9 | Val.: 97.12 -> 95.38 | Hurt |
| use a standard normal rather than fixed zero bridge prior (ablation) | GLAD · QM9 | Nov.: 38.75 -> 41.54 | Helped |
| use GLAD rather than DGAE | generic graph generation · Enzymes | AVG MMD: 0.025 -> 0.009 | Helped |
| use GLAD rather than DGAE | molecule generation · ZINC250k | FCD: 4.4 -> 2.54 | Helped |
Surprising findings
- Quantization is critical: removing it (unquantized discrete latent) drops QM9 FCD from 0.201 to 1.207 and validity from 97.12 to 83.12.
- On ZINC250k validity without correction is only 81.81%, below several baselines such as GDSS (97.01%), and on QM9 novelty is low (38.75%).
Limitations
- Validity on ZINC250k (81.81%) and novelty on QM9 (38.75%) are weaker than several baselines.
- Relies on hand-crafted structural and spectral input features (cycle counts, Laplacian spectra) and node degrees for generic graphs.
- Generic-graph results are reported only on three small datasets with generic MMD metrics.
Experimental setup
Datasets: Community-small Ego-small Enzymes QM9 ZINC250k
Benchmarks: Community-small Ego-small Enzymes QM9 ZINC250k
Metrics: MMD degree MMD clustering MMD orbit validity uniqueness novelty NSPDK FCD reconstruction accuracy
Baselines: GraphRNN GraphAF GDSS DiGress GraphArm GraphVAE GNF GraphDF DGAE MoFlow
Builds on: diffusion bridges finite scalar quantization straight-through estimator graph transformer DGAE
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