SimGFM: Simplifying Discrete Flow Matching for Graph Generation

Discrete Flow Matching (DFM) presents a promising approach for graph generation; however, existing adaptations often introduce substantial complexity by incorporating task-specific heuristics, compromising the continuity equation and significantly expanding the hyperparameter space. Moreover, their sampling efficiency remains limited, as the required number of steps is often comparable to diffusion models, diminishing DFM’s practical advantages. To address these limitations, we propose SimGFM, a simplified graph DFM for graph generation. Leveraging characteristic patterns in graph-generation trajectories, SimGFM relies only on the scheduler and rate matrix, eliminating heavy heuristics and hyperparameter tuning, and achieves large step reductions while preserving SOTA results. SimGFM achieves strong empirical results: on QM9, it matches prior models requiring 500–1000 steps with only 10 steps, and on most datasets, its performance at 50 steps matches or surpasses these baselines, demonstrating both efficiency and competitiveness. Our source code is available at https://github.com/LUOyk1999/SimGFM.

Graphs are a common way to represent connected systems, such as molecules, social networks, and other structured data. Generating realistic graphs is useful for scientific discovery and machine learning, but existing methods can be slow and complicated, often requiring many refinement steps and extensive tuning. We introduce SimGFM, a simpler and faster method for generating graphs. Instead of relying on multiple specialized design choices, SimGFM focuses on the essential process needed to gradually construct a graph. This makes the method easier to use and substantially reduces the number of generation steps. Across several benchmark datasets, SimGFM produces graphs of comparable or better quality than previous methods while using far fewer steps. For example, on a widely used molecular dataset, it achieves competitive performance with only 10 steps, whereas earlier methods typically require 500 to 1000 steps. These results suggest that high-quality graph generation can be made both simpler and more efficient, facilitating practical applications involving molecular structures and other network-based data.