Generating Directed Graphs with Dual Attention and Asymmetric Encoding

Abstract

Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, or visual understanding. Generating such graphs enables simulation, data augmentation and novel instance discovery; however, this task remains underexplored. We identify two key reasons: first, modeling edge directionality introduces a substantially larger dependency space, making the underlying distribution harder to learn; second, the absence of standardized benchmarks hinders rigorous evaluation. Addressing the former limitation requires more expressive models that are sensitive to directional topologies. Thus, we propose Directo, the first generative model for directed graphs built upon the discrete flow matching framework. Our approach combines: (i) a dual-attention mechanism distinctly capturing incoming and outgoing dependencies, (ii) a robust, discrete generative framework, and (iii) principled positional encodings tailored to asymmetric pairwise relations. To address the second limitation and support evaluation, we introduce a novel and extensive benchmark suite covering synthetic and real-world datasets. Experiments show that our method outperforms existing directed graph generation approaches across diverse settings and competes with specialized models for particular classes, such as directed acyclic graphs. These results highlight the effectiveness and generality of our approach, establishing a solid foundation for future research in directed graph generation.