# Tabular Diffusion Counterfactual Explanations

arXiv: https://arxiv.org/abs/2509.00876 · HTML: https://mlsanity.com/paper/2509.00876/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 46 of its 58 references that are in the map.
- First posted on arXiv 31 Aug 2025.

## Builds on (most cited first, 30 of 46)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Simple Guidance Mechanisms for Discrete Diffusion Models](https://mlsanity.com/paper/2412.10193/) (2024)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)

## Abstract (arXiv)

Counterfactual explanations methods provide an important tool in the field of interpretable machine learning. Recent advances in this direction have focused on diffusion models to explain a deep classifier. However, these techniques have predominantly focused on problems in computer vision. In this paper, we focus on tabular data typical in finance and the social sciences and propose a novel guided reverse process for categorical features based on an approximation to the Gumbel-softmax distribution. Furthermore, we study the effect of the temperature τ and derive a theoretical bound between the Gumbel-softmax distribution and our proposed approximated distribution. We perform experiments on several large-scale credit lending and other tabular datasets, assessing their performance in terms of the quantitative measures of interpretability, diversity, instability, and validity. These results indicate that our approach outperforms popular baseline methods, producing robust and realistic counterfactual explanations.