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When Edge Independence Fails: Joint Graph Diffusion with Latent Sociability Priors

NeurIPS 2026 · Graph learning › Graph self-supervised learning · approach: Diffusion-based graph generation

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Proposes Latent Sociability Prior (LSP) with a joint discrete-edge and Gaussian-latent diffusion over log-sociability variables, so graph diffusion escapes the Erdős–Rényi fixed point without node features.

Problem

Discrete graph diffusion with independent edge noise forces an Erdős–Rényi terminal prior, which makes any GNN denoiser approximately output E-R graphs in the large-graph limit, so unconditional generation without node features loses node heterogeneity and higher-order structure.

Approach

Co-diffuse continuous latent node log-sociability variables u_i with discrete edges; edge stationaries are pair-specific, p_ij = 1 - exp(-exp(u_i+u_j)), making the terminal prior an exchangeable but non-independent (inhomogeneous random graph) model, and the latent is set in closed form from centered log-degrees rather than via an encoder.

Key results

• On CoraChameleon-Node100 without features, JointLSP+DiGress reaches triangle MMD ratio 2.33 vs 14.82 for DiGress (no features), and assortativity 59.72 vs 101.95.
• At n=100, DiGress without features is better on degree (4.53 vs 10.50) and PLE (4.64 vs 10.79), which the authors attribute to over-correction of degree under LSP.
• JointLSP+DiGress (no features) outperforms DiGress with up to 10 structural features on clustering, triangles, and assortativity, but is still beaten by DiGress with spectral features (k=17).

Surprising findings

• Structural node features computed a posteriori offer only limited help because their standard deviation vanishes on near-E-R graphs, and DiGress with 10 structural features still underperforms the feature-free LSP variant on several higher-order statistics.
• At n=100, the LSP variant is worse than DiGress on degree distribution and PLE, which the authors attribute to degree over-correction.

Limitations

• Benefit expected to be minimal for graphs with rich node features (e.g., molecules).
• Spectral features still outperform the proposed method, and combining LSP with auxiliary features is unresolved.
• Sparse-regime approximations are used for the latent closed form and calibration of mu_LSP.

Experimental setup

Datasets: CoraChameleon (new, subgraphs of Cora and Chameleon) Ego Community

Benchmarks: CoraChameleon Ego Community

Metrics: MMD ratio degree distribution clustering coefficient triangle count degree assortativity power-law exponent characteristic path length

Baselines: DiGress DiGress + structural features DiGress + spectral features

Builds on: DiGress SparseDiff DDPM inhomogeneous random graph models Gaussian diffusion

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