# D4Explainer: In-Distribution GNN Explanations via Discrete Denoising Diffusion

arXiv: https://arxiv.org/abs/2310.19321 · HTML: https://mlsanity.com/paper/2310.19321/

## Key facts

- Cited by 9 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 50 of its 62 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## 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, 30 of 50)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [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)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Learning to Explain: An Information-Theoretic Perspective on Model Interpretation](https://mlsanity.com/paper/1802.07814/) (2018)
- [XGNN: Towards Model-Level Explanations of Graph Neural Networks](https://mlsanity.com/paper/2006.02587/) (2020)

## Built on by (most cited first, 9 of 9)

- [PowerGraph: A power grid benchmark dataset for graph neural networks](https://mlsanity.com/paper/2402.02827/) (2024)
- [A Directional Diffusion Graph Transformer for Recommendation](https://mlsanity.com/paper/2404.03326/) (2024)
- [Generative Explanations for Graph Neural Network: Methods and Evaluations](https://mlsanity.com/paper/2311.05764/) (2023)
- [Towards Comprehensive and Prerequisite-Free Explainer for Graph Neural Networks](https://mlsanity.com/paper/2505.14005/) (2025)
- [Discrete Diffusion-Based Model-Level Explanation of Heterogeneous GNNs with Node Features](https://mlsanity.com/paper/2508.08458/) (2025)
- [MUSE-Explainer: Counterfactual Explanations for Symbolic Music Graph Classification Models](https://mlsanity.com/paper/2509.26521/) (2025)
- [AIMing for Standardised Explainability Evaluation in GNNs: A Framework and Case Study on Graph Kernel Networks](https://mlsanity.com/paper/2605.14884/) (2026)
- [A Completion-Aware Framework for Impactful Counterfactual Explainability in Graph Neural Networks](https://mlsanity.com/paper/2606.22033/) (2026)
- [A Comparative Study of Counterfactual Explainers for Graph Neural Networks Enabling Multiple Types of Graph Edit](https://mlsanity.com/paper/2609.05113/) (2026)

## Abstract (arXiv)

The widespread deployment of Graph Neural Networks (GNNs) sparks significant interest in their explainability, which plays a vital role in model auditing and ensuring trustworthy graph learning. The objective of GNN explainability is to discern the underlying graph structures that have the most significant impact on model predictions. Ensuring that explanations generated are reliable necessitates consideration of the in-distribution property, particularly due to the vulnerability of GNNs to out-of-distribution data. Unfortunately, prevailing explainability methods tend to constrain the generated explanations to the structure of the original graph, thereby downplaying the significance of the in-distribution property and resulting in explanations that lack reliability. To address these challenges, we propose D4Explainer, a novel approach that provides in-distribution GNN explanations for both counterfactual and model-level explanation scenarios. The proposed D4Explainer incorporates generative graph distribution learning into the optimization objective, which accomplishes two goals: 1) generate a collection of diverse counterfactual graphs that conform to the in-distribution property for a given instance, and 2) identify the most discriminative graph patterns that contribute to a specific class prediction, thus serving as model-level explanations. It is worth mentioning that D4Explainer is the first unified framework that combines both counterfactual and model-level explanations. Empirical evaluations conducted on synthetic and real-world datasets provide compelling evidence of the state-of-the-art performance achieved by D4Explainer in terms of explanation accuracy, faithfulness, diversity, and robustness.