# Generating Directed Graphs with Dual Attention and Asymmetric Encoding

arXiv: https://arxiv.org/abs/2506.16404 · HTML: https://mlsanity.com/paper/2506.16404/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 92 references that are in the map.
- First posted on arXiv 19 Jun 2025.

## Builds on (most cited first, 30 of 67)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotations](https://mlsanity.com/paper/1602.07332/) (2016)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Image Generation from Scene Graphs](https://mlsanity.com/paper/1804.01622/) (2018)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)

## Built on by (most cited first, 3 of 3)

- [Principled Latent Diffusion for Graphs via Laplacian Autoencoders](https://mlsanity.com/paper/2601.13780/) (2026)
- [Balancing Symmetry and Efficiency in Graph Flow Matching](https://mlsanity.com/paper/2602.18084/) (2026)
- [Stable Transformers for Graph Generation](https://mlsanity.com/paper/2609.39739/) (2026)

## Abstract (arXiv)

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.