DiPhon: Diffusion on Graphons for Scalable Graph Generation

2026-07-09 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

DiPhon is a novel diffusion framework designed for scalable graph generation, specifically addressing the challenge of applying diffusion models to large graphs in dense-graph settings. It leverages graphons, size-agnostic limit objects of dense graph sequences, to study structural graph statistics across node-size scales. The framework formulates a continuous diffusion process on the graphon space via a Jacobi stochastic differential equation (SDE), then proposes a discretized graph-level process mimicking these dynamics on finite graphs. The reverse-time process is derived, with its marginal score admitting a tractable form estimated via graph denoising. DiPhon is proven to exactly match the first moment of marginal distributions induced by the continuous graphon process and approximates the second moment with a closed-form discrepancy. This enables training on small graphs (e.g., 20-80 nodes for trees, 40-80 for SBMs/PA) and generating significantly larger graphs (up to 300 nodes) without retraining, preserving core topological properties.

Key takeaway

For Machine Learning Engineers developing graph generative models, DiPhon offers a principled approach to overcome scalability limitations. You can train your models on smaller graph datasets and reliably generate significantly larger graphs, up to 300 nodes, without the need for costly retraining. This method, grounded in graphon theory and Jacobi SDEs, ensures structural property preservation, making it ideal for applications like molecular design where size transferability is crucial.

Key insights

Graphons enable scalable graph diffusion models to generalize from small to large graphs without retraining.

Principles

• Graphons enable size-agnostic graph representations.
• Jacobi SDEs keep edge probabilities bounded in [0,1].
• Moment matching ensures discrete process fidelity.

Method

DiPhon formulates a Jacobi SDE on graphon space, discretizes it for finite graphs, and estimates the reverse-time marginal score via a graph neural network trained with a binary denoising loss.

In practice

• Train diffusion models on small graphs for large-scale inference.
• Use Jacobi SDEs for bounded-domain diffusion tasks.
• Apply graph denoising for score estimation in reverse SDEs.

Topics

• Graph Generative Models
• Diffusion Models
• Graphons
• Scalable Graph Generation
• Jacobi SDEs
• Graph Neural Networks

Best for: AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.