Generating Directed Graphs with Dual Attention and Asymmetric Encoding

TL;DR

This paper introduces Directo, a novel generative model for directed graphs that employs dual attention and asymmetric encoding, addressing the challenges of modeling edge directionality and lacking benchmarks in the field.

Contribution

We propose Directo, the first directed graph generative model based on discrete flow matching, with specialized positional encodings and dual attention mechanisms.

Findings

Performs well across synthetic and real-world datasets

Competitively models directed acyclic graphs

Establishes a new benchmark suite for evaluation

Abstract

Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, and visual understanding. Generating such graphs enables tasks such as simulation, data augmentation and novel instance discovery; however, directed graph generation remains underexplored. We identify two key factors limiting progress in this direction: 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 requires more expressive models that are sensitive to directional topologies. We propose Directo, the first generative model for directed graphs built upon the discrete flow matching framework. Our approach combines: (i) principled positional encodings tailored to asymmetric pairwise relations, (ii) a dual-attention mechanism capturing both incoming and outgoing dependencies, and (iii) a robust, discrete generative framework. To support evaluation, we introduce a benchmark suite covering synthetic and real-world datasets. It shows that our method performs strongly across diverse settings and even competes with specialized models for particular classes, such as directed acyclic graphs. Our results highlight the effectiveness and generality of our approach, establishing a solid foundation for future research in directed graph generation.