DeFoG: Discrete Flow Matching for Graph Generation

Graph generative models are essential across diverse scientific domains by capturing complex distributions over relational data. Among them, graph diffusion models achieve superior performance but face inefficient sampling and limited flexibility due to the tight coupling between training and sampling stages. We introduce DeFoG, a novel graph generative framework that disentangles sampling from training, enabling a broader design space for more effective and efficient model optimization. DeFoG employs a discrete flow-matching formulation that respects the inherent symmetries of graphs. We theoretically ground this disentangled formulation by explicitly relating the training loss to the sampling algorithm and showing that DeFoG faithfully replicates the ground truth graph distribution. Building on these foundations, we thoroughly investigate DeFoG's design space and propose novel sampling methods that significantly enhance performance and reduce the required number of refinement steps. Extensive experiments demonstrate state-of-the-art performance across synthetic, molecular, and digital pathology datasets, covering both unconditional and conditional generation settings. It also outperforms most diffusion-based models with just 5–10\% of their sampling steps.

Graphs are a powerful way to represent relationships, such as atoms in a molecule, people in a social network, or roads in a city. Being able to generate new graphs helps researchers design novel drugs, discover new materials, and better understand social or transportation systems.We introduce a new method called DeFoG that teaches computers to generate graphs more efficiently and accurately. Instead of relying on traditional step-by-step recipes, DeFoG learns how to gradually transform random noise into a realistic graph, like carving a sculpture from a block of marble. This makes the generation process faster and more reliable. DeFoG is also designed to be flexible, performing well across different kinds of graphs. It focuses on the structure of the graph itself, rather than arbitrary choices like the order in which the nodes are named. This helps it generalize more easily to different applications.We test DeFoG in a range of settings, including real-world problems such as molecular generation and digital pathology, and show that it creates more accurate graphs in less time. This opens up new possibilities in fields like chemistry, biology, and network design.