# Navigating the Structured What-If Spaces: Counterfactual Generation via Structured Diffusion

arXiv: https://arxiv.org/abs/2312.13616 · HTML: https://mlsanity.com/paper/2312.13616/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 32 of its 44 references that are in the map.
- First posted on arXiv 21 Dec 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 32)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Adversarial Examples for Evaluating Reading Comprehension Systems](https://mlsanity.com/paper/1707.07328/) (2017)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [Adversarial Example Generation with Syntactically Controlled Paraphrase Networks](https://mlsanity.com/paper/1804.06059/) (2018)
- [Understanding Neural Networks through Representation Erasure](https://mlsanity.com/paper/1612.08220/) (2016)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Model-Agnostic Interpretability of Machine Learning](https://mlsanity.com/paper/1606.05386/) (2016)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Explaining Black Box Predictions and Unveiling Data Artifacts through Influence Functions](https://mlsanity.com/paper/2005.06676/) (2020)
- [Pathologies of Neural Models Make Interpretations Difficult](https://mlsanity.com/paper/1804.07781/) (2018)
- [Explaining NLP Models via Minimal Contrastive Editing (MiCE)](https://mlsanity.com/paper/2012.13985/) (2020)
- [Diffusion Visual Counterfactual Explanations](https://mlsanity.com/paper/2210.11841/) (2022)
- [Grounding Visual Explanations](https://mlsanity.com/paper/1807.09685/) (2018)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Diffusion Models for Counterfactual Explanations](https://mlsanity.com/paper/2203.15636/) (2022)
- [Generate Your Counterfactuals: Towards Controlled Counterfactual Generation for Text](https://mlsanity.com/paper/2012.04698/) (2020)
- [Contrastive Explanations for Model Interpretability](https://mlsanity.com/paper/2103.01378/) (2021)
- [Model Agnostic Contrastive Explanations for Structured Data](https://mlsanity.com/paper/1906.00117/) (2019)
- [Sparse Visual Counterfactual Explanations in Image Space](https://mlsanity.com/paper/2205.07972/) (2022)
- [NeuroCounterfactuals: Beyond Minimal-Edit Counterfactuals for Richer Data Augmentation](https://mlsanity.com/paper/2210.12365/) (2022)
- [MACE: An Efficient Model-Agnostic Framework for Counterfactual Explanation](https://mlsanity.com/paper/2205.15540/) (2022)

## Built on by (most cited first, 5 of 5)

- [Tabular Diffusion based Actionable Counterfactual Explanations for Network Intrusion Detection](https://mlsanity.com/paper/2507.17161/) (2025)
- [Tabular Diffusion Counterfactual Explanations](https://mlsanity.com/paper/2509.00876/) (2025)
- [TabChange: Precise Attribute Changes in Tabular Data](https://mlsanity.com/paper/2606.00503/) (2026)
- [Agentic Search for Counterfactual Recourse under Fixed LLM Budgets](https://mlsanity.com/paper/2606.08696/) (2026)
- [Explanations-Driven Active Feature Acquisition for Algorithmic Recourse](https://mlsanity.com/paper/2609.12179/) (2026)

## Abstract (arXiv)

Generating counterfactual explanations is one of the most effective approaches for uncovering the inner workings of black-box neural network models and building user trust. While remarkable strides have been made in generative modeling using diffusion models in domains like vision, their utility in generating counterfactual explanations in structured modalities remains unexplored. In this paper, we introduce Structured Counterfactual Diffuser or SCD, the first plug-and-play framework leveraging diffusion for generating counterfactual explanations in structured data. SCD learns the underlying data distribution via a diffusion model which is then guided at test time to generate counterfactuals for any arbitrary black-box model, input, and desired prediction. Our experiments show that our counterfactuals not only exhibit high plausibility compared to the existing state-of-the-art but also show significantly better proximity and diversity.