Generating Directed Graphs with Dual Attention and Asymmetric Encoding

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, yet it remains underexplored. A key challenge lies in modeling edge directionality, which greatly enlarges the dependency space and makes the underlying distribution harder to learn. Addressing this requires more expressive models that are sensitive to directional topologies. We propose Directo, the first generative model for directed graphs built on 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. Our method performs strongly in diverse settings and even competes with specialized models for particular classes, such as directed acyclic graphs, highlighting the effectiveness and generality of our approach, and establishing a solid foundation for future research in directed graph generation.