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Editing Partially Observable Networks via Graph Diffusion Models
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Proposes SGDM, a subgraph-based graph diffusion framework that trains on subgraphs sampled from a single partially observed network to support expansion, denoising, and attribute-based style transfer editing.
Problem
Refining a single noisy, incomplete observed network (denoising, expansion, attribute editing) with graph diffusion models, which normally need many clean graphs and scale quadratically with node count.
Approach
Sample ego-network subgraphs from one large graph, train any graph diffusion backbone (DiGRESS, EDGE, GDSS) on the subgraph collection with global Laplacian positional context, and edit by in-painting-style reverse-process constraints (expansion, denoising) or regressor classifier guidance (style transfer).
Key results
- On BA-Shapes denoising, SGDM with EDGE backbone reaches diversity 0.992 and edge overlap 0.3427 versus EDGE's 0.834 and 0.0427 without sampling.
- Adding global Laplacian positional context to SGDM reduces Sum-Degree style-transfer MAE from 6.46 to 3.78 (GCN regressor) on BA-Shapes.
- Expansion results are weak: consensus is near 0 across datasets for most SGDM variants, which the authors attribute to degree-distribution guidance in EDGE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use subgraph sampling instead of learning directly on one graph (ablation) | EDGE for denoising · Cora | Sparsity: 0.115 -> 0.591 | Helped |
| Use subgraph sampling instead of learning directly on one graph (ablation) | EDGE for denoising · PolBlogs | Sparsity: 0.0411 -> 0.340 | Helped |
| Use subgraph sampling instead of learning directly on one graph (ablation) | EDGE for expansion · Cora | Consensus: 0.000 -> 0.000 | No clear effect |
| Use global context with subgraph sampling (ablation) | SGDM + EDGE for denoising · Cora | Sparsity: 0.591 -> 0.442 | Helped |
| Use global context with subgraph sampling (ablation) | SGDM + EDGE for denoising · PolBlogs | Sparsity: 0.340 -> 0.640 | Helped |
| Use global context with subgraph sampling (ablation) | SGDM + EDGE for expansion · Cora | Consensus: 0.000 -> 0.000 | No clear effect |
| Add global context (ablation) | DiGRESS + SGDM with GCN regressor · BA-Shapes style transfer: Sum-Degree | MAE: 6.46 -> 3.78 | Helped |
| Add global context (ablation) | DiGRESS + SGDM with GIN regressor · BA-Shapes style transfer: Max-Degree | MAE: 45.09 -> 11.04 | Helped |
| Add global context (ablation) | DiGRESS + SGDM with GCN regressor · BA-Shapes style transfer: Num. Triangles | MAE: 9.18 -> 19.6 | Hurt |
Surprising findings
- Expansion performance is poor for most variants, with near-zero consensus, and the authors attribute this to degree-distribution guidance in the EDGE backbone.
- Global context did not help changing the number of triangles; Num. Triangles MAE rose from about 9-10 without context to 19.6 with context.
Limitations
- No direct baselines exist for single-network editing, so comparisons rely on adapted EDGE only.
- Evaluation uses only synthetic corruptions and does not measure downstream task performance.
- Global context hurts triangle-count style transfer.
Experimental setup
Datasets: BA-Shapes PolBlogs CORA
Benchmarks: BA-Shapes PolBlogs CORA
Metrics: consensus edge overlap diversity sparsity mean absolute error for style transfer
Baselines: EDGE
Builds on: DiGRESS EDGE GDSS Lugmayr et al. RePaint in-painting classifier guidance
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- SBGD: Improving Graph Diffusion Generative Model via Stochastic Block Diffusion (ICML 2025 · similarity 0.87)
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