# DeFoG: Discrete Flow Matching for Graph Generation

arXiv: https://arxiv.org/abs/2410.04263 · HTML: https://mlsanity.com/paper/2410.04263/

## Key facts

- Cited by 82 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 0 of its 81 references that are in the map.
- First posted on arXiv 5 Oct 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Built on by (most cited first, 30 of 82)

- [Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms](https://mlsanity.com/paper/2502.00234/) (2025)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [Flow Matching Meets Biology and Life Science: A Survey](https://mlsanity.com/paper/2507.17731/) (2025)
- [A Theoretical Analysis of Discrete Flow Matching Generative Models](https://mlsanity.com/paper/2509.22623/) (2025)
- [Bures-Wasserstein Flow Matching for Graph Generation](https://mlsanity.com/paper/2506.14020/) (2025)
- [Error Analysis of Discrete Flow with Generator Matching](https://mlsanity.com/paper/2509.21906/) (2025)
- [HOG-Diff: Higher-Order Guided Diffusion for Graph Generation](https://mlsanity.com/paper/2502.04308/) (2025)
- [FragFM: Hierarchical Framework for Efficient Molecule Generation via Fragment-Level Discrete Flow Matching](https://mlsanity.com/paper/2502.15805/) (2025)
- [Learning Flexible Forward Trajectories for Masked Molecular Diffusion](https://mlsanity.com/paper/2505.16790/) (2025)
- [Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation](https://mlsanity.com/paper/2602.15022/) (2026)
- [Discrete Guidance Matching: Exact Guidance for Discrete Flow Matching](https://mlsanity.com/paper/2509.21912/) (2025)
- [Flow Matching for Offline Reinforcement Learning with Discrete Actions](https://mlsanity.com/paper/2602.06138/) (2026)
- [Categorical Schr"odinger Bridge Matching](https://mlsanity.com/paper/2502.01416/) (2025)
- [Graph-GRPO: Training Graph Flow Models with Reinforcement Learning](https://mlsanity.com/paper/2603.10395/) (2026)
- [Principled Latent Diffusion for Graphs via Laplacian Autoencoders](https://mlsanity.com/paper/2601.13780/) (2026)
- [Prior-Informed Flow Matching for Graph Reconstruction](https://mlsanity.com/paper/2601.22107/) (2026)
- [GGBall: Graph Generative Model on Poincar'e Ball](https://mlsanity.com/paper/2506.07198/) (2025)
- [Generating Directed Graphs with Dual Attention and Asymmetric Encoding](https://mlsanity.com/paper/2506.16404/) (2025)
- [Corrected Samplers for Discrete Flow Models](https://mlsanity.com/paper/2601.22519/) (2026)
- [Order Matters in Retrosynthesis: Structure-aware Generation via Reaction-Center-Guided Discrete Flow Matching](https://mlsanity.com/paper/2602.13136/) (2026)
- [Flowette: Flow Matching with Graphette Priors for Graph Generation](https://mlsanity.com/paper/2602.23566/) (2026)
- [Discrete Flow Matching Policy Optimization](https://mlsanity.com/paper/2604.06491/) (2026)
- [Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once](https://mlsanity.com/paper/2605.08424/) (2026)
- [A Diffusive Data Augmentation Framework for Reconstruction of Complex Network Evolutionary History](https://mlsanity.com/paper/2501.06485/) (2025)
- [Fast Graph Generation via Autoregressive Noisy Filtration Modeling](https://mlsanity.com/paper/2502.02415/) (2025)
- [Composable Score-based Graph Diffusion Model for Multi-Conditional Molecular Generation](https://mlsanity.com/paper/2509.09451/) (2025)
- [Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction](https://mlsanity.com/paper/2510.04522/) (2025)
- [LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarsening](https://mlsanity.com/paper/2512.01190/) (2025)
- [FlowMS: Flow Matching for De Novo Structure Elucidation from Mass Spectra](https://mlsanity.com/paper/2603.18397/) (2026)
- [Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generation](https://mlsanity.com/paper/2603.28572/) (2026)

## Abstract (arXiv)

Graph generative models are essential across diverse scientific domains by capturing complex distributions over relational data. Among them, graph diffusion models achieve superior performance but face inefficient sampling and limited flexibility due to the tight coupling between training and sampling stages. We introduce DeFoG, a novel graph generative framework that disentangles sampling from training, enabling a broader design space for more effective and efficient model optimization. DeFoG employs a discrete flow-matching formulation that respects the inherent symmetries of graphs. We theoretically ground this disentangled formulation by explicitly relating the training loss to the sampling algorithm and showing that DeFoG faithfully replicates the ground truth graph distribution. Building on these foundations, we thoroughly investigate DeFoG's design space and propose novel sampling methods that significantly enhance performance and reduce the required number of refinement steps. Extensive experiments demonstrate state-of-the-art performance across synthetic, molecular, and digital pathology datasets, covering both unconditional and conditional generation settings. It also outperforms most diffusion-based models with just 5-10% of their sampling steps.