# Diffeomorphic Counterfactuals with Generative Models

arXiv: https://arxiv.org/abs/2206.05075 · HTML: https://mlsanity.com/paper/2206.05075/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 70 of its 119 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 30 of 70)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [InterFaceGAN: Interpreting the Disentangled Face Representation Learned by GANs](https://mlsanity.com/paper/2005.09635/) (2020)

## Built on by (most cited first, 29 of 29)

- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [Decoupling Pixel Flipping and Occlusion Strategy for Consistent XAI Benchmarks](https://mlsanity.com/paper/2401.06654/) (2024)
- [Disentangled Explanations of Neural Network Predictions by Finding Relevant Subspaces](https://mlsanity.com/paper/2212.14855/) (2022)
- [Towards Fixing Clever-Hans Predictors with Counterfactual Knowledge Distillation](https://mlsanity.com/paper/2310.01011/) (2023)
- [Probabilistically Plausible Counterfactual Explanations with Normalizing Flows](https://mlsanity.com/paper/2405.17640/) (2024)
- [Preemptively Pruning Clever-Hans Strategies in Deep Neural Networks](https://mlsanity.com/paper/2304.05727/) (2023)
- [Counterfactual Explanations via Riemannian Latent Space Traversal](https://mlsanity.com/paper/2411.02259/) (2024)
- [Symmetry Discovery for Different Data Types](https://mlsanity.com/paper/2410.09841/) (2024)
- [Towards Desiderata-Driven Design of Visual Counterfactual Explainers](https://mlsanity.com/paper/2506.14698/) (2025)
- [Mitigating Clever Hans Strategies in Image Classifiers through Generating Counterexamples](https://mlsanity.com/paper/2510.17524/) (2025)
- [Generating Likely Counterfactuals Using Sum-Product Networks](https://mlsanity.com/paper/2401.14086/) (2024)
- [Diffusion Counterfactuals for Image Regressors](https://mlsanity.com/paper/2503.20595/) (2025)
- [LeapFactual: Reliable Visual Counterfactual Explanation Using Conditional Flow Matching](https://mlsanity.com/paper/2510.14623/) (2025)
- [Equivariant Neural Tangent Kernels](https://mlsanity.com/paper/2406.06504/) (2024)
- [Graph Diffusion Counterfactual Explanation](https://mlsanity.com/paper/2511.16287/) (2025)
- [Visual Disentangled Diffusion Autoencoders: Scalable Counterfactual Generation for Foundation Models](https://mlsanity.com/paper/2601.21851/) (2026)
- [Counterfactual Activation Editing for Post-hoc Prosody and Mispronunciation Correction in TTS Models](https://mlsanity.com/paper/2506.00832/) (2025)
- [Protein Counterfactuals via Diffusion-Guided Latent Optimization](https://mlsanity.com/paper/2603.10811/) (2026)
- [SCE-LITE-HQ: Smooth visual counterfactual explanations with generative foundation models](https://mlsanity.com/paper/2603.17048/) (2026)
- [Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI](https://mlsanity.com/paper/2411.15265/) (2024)
- [Counterfactual Explanations on Robust Perceptual Geodesics](https://mlsanity.com/paper/2601.18678/) (2026)
- [Manifold-Aligned Guided Integrated Gradients for Reliable Feature Attribution](https://mlsanity.com/paper/2605.02167/) (2026)
- [Faithful, Sufficient and Understandable: Rethinking Graph Counterfactual Explanations via Discrete Diffusion Inversion](https://mlsanity.com/paper/2608.12083/) (2026)
- [Adversarial Purification by Consistency-aware Latent Space Optimization on Data Manifolds](https://mlsanity.com/paper/2412.08394/) (2024)
- [RIE-SenseNet: Riemannian Manifold Embedding of Multi-Source Industrial Sensor Signals for Robust Pattern Recognition](https://mlsanity.com/paper/2502.02428/) (2025)
- [Residual-Space Evolutionary Optimization via Flow-based Generative Models](https://mlsanity.com/paper/2606.20084/) (2026)
- [Diffeomorphic Optimization](https://mlsanity.com/paper/2607.00947/) (2026)
- [Explaining Hyperbolic Neural Networks via Geometry-Aware Relevance Propagation](https://mlsanity.com/paper/2609.35128/) (2026)
- [Towards Fast and Disentangled Counterfactuals for Visual Foundation Models](https://mlsanity.com/paper/2610.00895/) (2026)

## Abstract (arXiv)

Counterfactuals can explain classification decisions of neural networks in a human interpretable way. We propose a simple but effective method to generate such counterfactuals. More specifically, we perform a suitable diffeomorphic coordinate transformation and then perform gradient ascent in these coordinates to find counterfactuals which are classified with great confidence as a specified target class. We propose two methods to leverage generative models to construct such suitable coordinate systems that are either exactly or approximately diffeomorphic. We analyze the generation process theoretically using Riemannian differential geometry and validate the quality of the generated counterfactuals using various qualitative and quantitative measures.