# Mitigating topology biases in Graph Diffusion via Counterfactual Intervention

arXiv: https://arxiv.org/abs/2603.02005 · HTML: https://mlsanity.com/paper/2603.02005/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 22 of its 39 references that are in the map.
- First posted on arXiv 2 Mar 2026.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (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)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Say No to the Discrimination: Learning Fair Graph Neural Networks with Limited Sensitive Attribute Information](https://mlsanity.com/paper/2009.01454/) (2020)
- [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [Generative Diffusion Models on Graphs: Methods and Applications](https://mlsanity.com/paper/2302.02591/) (2023)
- [Diffusion Models for Graphs Benefit From Discrete State Spaces](https://mlsanity.com/paper/2210.01549/) (2022)
- [Learning from Counterfactual Links for Link Prediction](https://mlsanity.com/paper/2106.02172/) (2021)
- [FairDrop: Biased Edge Dropout for Enhancing Fairness in Graph Representation Learning](https://mlsanity.com/paper/2104.14210/) (2021)
- [Generative Code Modeling with Graphs](https://mlsanity.com/paper/1805.08490/) (2018)
- [Fast Graph Generation via Spectral Diffusion](https://mlsanity.com/paper/2211.08892/) (2022)
- [Unbiased Graph Embedding with Biased Graph Observations](https://mlsanity.com/paper/2110.13957/) (2021)
- [Towards Fair Graph Neural Networks via Graph Counterfactual](https://mlsanity.com/paper/2307.04937/) (2023)
- [A Survey on Fairness for Machine Learning on Graphs](https://mlsanity.com/paper/2205.05396/) (2022)
- [NVDiff: Graph Generation through the Diffusion of Node Vectors](https://mlsanity.com/paper/2211.10794/) (2022)
- [Graph Learning with Localized Neighborhood Fairness](https://mlsanity.com/paper/2212.12040/) (2022)
- [Privacy-Preserving Graph Machine Learning from Data to Computation: A Survey](https://mlsanity.com/paper/2307.04338/) (2023)
- [Neural Graph Generator: Feature-Conditioned Graph Generation using Latent Diffusion Models](https://mlsanity.com/paper/2403.01535/) (2024)

## Abstract (arXiv)

Graph diffusion models have gained significant attention in graph generation tasks, but they often inherit and amplify topology biases from sensitive attributes (e.g. gender, age, region), leading to unfair synthetic graphs. Existing fair graph generation using diffusion models is limited to specific graph-based applications with complete labels or requires simultaneous updates for graph structure and node attributes, making them unsuitable for general usage. To relax these limitations by applying the debiasing method directly on graph topology, we propose Fair Graph Diffusion Model (FairGDiff), a counterfactual-based one-step solution that mitigates topology biases while balancing fairness and utility. In detail, we construct a causal model to capture the relationship between sensitive attributes, biased link formation, and the generated graph structure. By answering the counterfactual question "Would the graph structure change if the sensitive attribute were different?", we estimate an unbiased treatment and incorporate it into the diffusion process. FairGDiff integrates counterfactual learning into both forward diffusion and backward denoising, ensuring that the generated graphs are independent of sensitive attributes while preserving structural integrity. Extensive experiments on real-world datasets demonstrate that FairGDiff achieves a superior trade-off between fairness and utility, outperforming existing fair graph generation methods while maintaining scalability.