SimGFM: Simplifying Discrete Flow Matching for Graph Generation

Chunyu Luo, Yuankai Luo, Xiao-Ming Wu, Lei Shi

Keywords: Graph Generation, Discrete Flow Models, Flow Matching

TL;DR: SimGFM achieves competitive graph generation in 10–50 steps through a principled, heuristic-free probabilistic design.

Abstract:

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. SimGFM introduces a graph-structured rate formulation based on minimalist design principles—characterized by a clear mathematical expression, free of ad-hoc heuristics, consistent with the continuity equation; along with a targeted scheduler informed by our observation that, under uniform denoising, valid graph structures predominantly emerge near the end of the denoising trajectory. 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.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 18431