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Advancing Graph Generation through Beta Diffusion
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Introduces Graph Beta Diffusion (GBD), a graph generative model built on beta diffusion that jointly models discrete adjacency and bounded continuous node features, with a degree/centrality-based concentration modulation to stabilize topology formation.
Problem
Graph diffusion models rely on Gaussian or categorical processes that poorly fit the mixed discrete and continuous, sparse, bounded, skewed node/edge statistics of graph data.
Approach
Use a multiplicative beta diffusion process (thinning/thickening of beta random variables) for both adjacency and node features, with a concentration-modulation technique that assigns higher concentration to important edges/nodes (high-centrality or carbon-bond) so key topology emerges early in the reverse chain, plus logit-domain computation and neural-network preconditioning.
Key results
- On Grid, GBD reaches degree MMD 0.045 versus 0.111 for GDSS and 0.144 for Wave-GD, and GBD is best on Ego-small degree MMD (0.011 vs 0.012 for Wave-GD).
- On QM9, GBD reports 99.88% validity and FCD 0.093, versus 99.69% and 0.108 for GruM; on ZINC250k, GBD's FCD 2.248 is the best but its validity 97.87% trails GruM's 98.65%.
- On Planar, GBD reports V.U.N. 92.5 versus 90.0 for GruM, and on SBM its V.U.N. is 75.0 versus 85.0 for GruM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use beta diffusion with GBD instead of Wave-GD | generic graph generation · Ego-small | Deg. MMD: 0.012 -> 0.011 | Helped |
| use beta diffusion with GBD instead of Wave-GD | generic graph generation · Community-small | Deg. MMD: 0.007 -> 0.002 | Helped |
| use beta diffusion with GBD instead of GDSS | generic graph generation · Grid | Deg. MMD: 0.111 -> 0.045 | Helped |
| use beta diffusion with GBD instead of GruM | graph generation · Planar | V.U.N.: 90.0 -> 92.5 | Helped |
| use beta diffusion with GBD instead of GruM | graph generation · SBM | V.U.N.: 85.0 -> 75.0 | Hurt |
| use beta diffusion with GBD instead of GruM | molecule generation · QM9 | Valid (%): 99.69 -> 99.88 | Helped |
| use beta diffusion with GBD instead of GruM | molecule generation · ZINC250k | FCD: 2.257 -> 2.248 | Helped |
| add preconditioning without logit-domain computation (ablation) | GBD · Ego-small | Deg. MMD: 0.015 -> 0.013 | Helped |
| add preconditioning without logit-domain computation (ablation) | GBD · Community-small | Deg. MMD: 0.010 -> 0.004 | Helped |
| add logit-domain computation while using preconditioning (ablation) | GBD · Ego-small | Deg. MMD: 0.013 -> 0.011 | Helped |
| add logit-domain computation while using preconditioning (ablation) | GBD · Community-small | Deg. MMD: 0.004 -> 0.002 | Helped |
| remove concentration modulation (ablation) | GBD · Planar | Orbit. MMD: 0.0135 -> 0.0294 | Hurt |
Surprising findings
- Concentration modulation based on degree centrality improved Planar and SBM metrics, but the authors note GBD only reaches comparable, not uniformly superior, results to GruM on SBM V.U.N.
Limitations
- Concentration modulation uses hand-chosen eta levels and assignment functions, which require domain knowledge (e.g., carbon bonds for molecules).
- On SBM V.U.N. and some molecule metrics GBD trails GruM or DiGress, so it is not uniformly best.
Experimental setup
Datasets: Ego-small Community-small Grid Planar SBM QM9 ZINC250k
Benchmarks: Ego-small Community-small Grid Planar SBM QM9 ZINC250k
Metrics: MMD degree MMD clustering coefficient MMD orbit count MMD Laplacian spectrum V.U.N. Valid % FCD NSPDK Scaffold similarity
Baselines: DeepGMG GraphRNN GraphAF GraphDF GraphVAE GNF EDP-GNN GDSS GDSS+TF GruM ConGress DiGress
Builds on: beta diffusion GDSS DiGress GruM Graph Transformer
Closest papers by meaning
- SBGD: Improving Graph Diffusion Generative Model via Stochastic Block Diffusion (ICML 2025 · similarity 0.91)
- Pard: Permutation-Invariant Autoregressive Diffusion for Graph Generation (NeurIPS 2024 · similarity 0.90)
- Discrete-state Continuous-time Diffusion for Graph Generation (NeurIPS 2024 · similarity 0.90)
- Graph Generation with Diffusion Mixture (ICML 2024 · similarity 0.90)
- Generating Graphs via Spectral Diffusion (ICLR 2025 · similarity 0.89)
- Generative Modelling of Structurally Constrained Graphs (NeurIPS 2024 · similarity 0.89)
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