DiPhon: New diffusion method generates arbitrarily large graphs without retraining
Train on tiny graphs, generate massive ones—DiPhon scales graph generation seamlessly.
Graph generation is critical for molecular design and network analysis, but scaling diffusion models to large graphs remains a challenge. DiPhon, developed by Sergio Rozada and colleagues, tackles this by leveraging graphons—size-agnostic limit objects of dense graph sequences. The framework defines a continuous diffusion process on graphon space via a Jacobi stochastic differential equation (SDE), then discretizes it into a graph-level process that mimics those dynamics on finite graphs. A key innovation is that the reverse-time process requires only the marginal score, which for the Jacobi process has a tractable form estimated via graph denoising.
DiPhon provably matches the first moment of the continuous graphon process exactly and approximates the second moment with a closed-form discrepancy. Empirically, the method demonstrates remarkable scalability: trained on small graphs (e.g., 50 nodes), it can generate graphs of 500 or more nodes at inference without retraining, preserving topological properties such as degree distribution and clustering coefficients. This opens the door to efficient, size-agnostic graph generation for applications in drug discovery, social network modeling, and beyond.
- DiPhon uses graphons (size-agnostic limit objects) to enable scalable graph generation across node counts.
- The Jacobi SDE formulation yields a tractable score, allowing training on small graphs and inference on much larger ones without retraining.
- Provably matches exact first moment and approximates second moment of the continuous graphon process, preserving core topological properties.
Why It Matters
Enables scalable graph generation for molecular design and network analysis without retraining on larger graphs.