mlsanityData to 7 Oct 2026

Diffusion Causal Models for Counterfactual Estimation

arXiv 2202.10166 ↗First posted 21 Feb 2022cs.LG cs.CVcited by 87

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Cited by 27 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

We consider the task of counterfactual estimation from observational imaging data given a known causal structure. In particular, quantifying the causal effect of interventions for high-dimensional data with neural networks remains an open challenge. Herein we propose Diff-SCM, a deep structural causal model that builds on recent advances of generative energy-based models. In our setting, inference is performed by iteratively sampling gradients of the marginal and conditional distributions entailed by the causal model. Counterfactual estimation is achieved by firstly inferring latent variables with deterministic forward diffusion, then intervening on a reverse diffusion process using the gradients of an anti-causal predictor w.r.t the input. Furthermore, we propose a metric for evaluating the generated counterfactuals. We find that Diff-SCM produces more realistic and minimal counterfactuals than baselines on MNIST data and can also be applied to ImageNet data. Code is available https://github.com/vios-s/Diff-SCM.

Key facts. Cited by 87 papers in the map (data through 7 Oct 2026). Builds on 34 of its 60 references that are in the map. First posted on arXiv 21 Feb 2022.

Builds on

34 of 60 references.

References · 34

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2020Denoising Diffusion Implicit Modelscited by 9,655
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  6. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  7. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  8. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  9. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  10. 2018Neural Ordinary Differential Equationscited by 3,733
  11. 2017Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPRcited by 1,086
  12. 2017Counterfactual Fairnesscited by 802
22 more
  1. 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 408
  2. 2019Your Classifier is Secretly an Energy Based Model and You Should Treat it Like Onecited by 402
  3. 2016Learning Representations for Counterfactual Inferencecited by 327
  4. 2019Counterfactual Visual Explanationscited by 312
  5. 2019Adapting Neural Networks for the Estimation of Treatment Effectscited by 285
  6. 2019Interpretable Counterfactual Explanations Guided by Prototypescited by 223
  7. 2020Deep Structural Causal Models for Tractable Counterfactual Inferencecited by 210
  8. 2021Counterfactual Generative Networkscited by 111
  9. 2021The Causal-Neural Connection: Expressiveness, Learnability, and Inferencecited by 97
  10. 2021D2C: Diffusion-Denoising Models for Few-shot Conditional Generationcited by 96
  11. 2019Image Counterfactual Sensitivity Analysis for Detecting Unintended Biascited by 74
  12. 2020Explaining The Efficacy of Counterfactually Augmented Datacited by 64
  13. 2020Sample-Efficient Reinforcement Learning via Counterfactual-Based Data Augmentationcited by 57
  14. 2020Evaluating and Mitigating Bias in Image Classifiers: A Causal Perspective Using Counterfactualscited by 56
  15. 2014From Ordinary Differential Equations to Structural Causal Models: the deterministic casecited by 41
  16. 2021Generating Interpretable Counterfactual Explanations By Implicit Minimisation of Epistemic and Aleatoric Uncertaintiescited by 41
  17. 2021Relating Graph Neural Networks to Structural Causal Modelscited by 39
  18. 2018Benchmarking Framework for Performance-Evaluation of Causal Inference Analysiscited by 33
  19. 2016From Deterministic ODEs to Dynamic Structural Causal Modelscited by 32
  20. 2019Adversarial Balancing-based Representation Learning for Causal Effect Inference with Observational Datacited by 29
  21. 2021ECINN: Efficient Counterfactuals from Invertible Neural Networkscited by 26
  22. 2018Generalization in anti-causal learningcited by 23

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 11; 2023: 22; 2024: 17; 2025: 20; 2026: 17.

87 papers.

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  1. 2022Diffusion Models in Vision: A Surveycited by 1,008
  2. 2022Diffusion Models for Medical Image Analysis: A Comprehensive Surveycited by 269
  3. 2022A Survey on Generative Diffusion Modelcited by 238
  4. 2022GENIE: Higher-Order Denoising Diffusion Solverscited by 127
  5. 2023Explainable Artificial Intelligence (XAI) 2.0: A Manifesto of Open Challenges and Interdisciplinary Research Directionscited by 123
  6. 2022Causal Machine Learning for Healthcare and Precision Medicinecited by 68
  7. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 64
  8. 2023High Fidelity Image Counterfactuals with Probabilistic Causal Modelscited by 53
  9. 2022What is Healthy? Generative Counterfactual Diffusion for Lesion Localizationcited by 52
  10. 2024Balancing Act: Distribution-Guided Debiasing in Diffusion Modelscited by 50
  11. 2023Causal normalizing flows: from theory to practicecited by 49
  12. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
38 more
  1. 2023Fast Diffusion-Based Counterfactuals for Shortcut Removal and Generationcited by 41
  2. 2023Measuring axiomatic soundness of counterfactual image modelscited by 34
  3. 2024On the Challenges and Opportunities in Generative AIcited by 31
  4. 2022Sparse Visual Counterfactual Explanations in Image Spacecited by 30
  5. 2023BiomedJourney: Counterfactual Biomedical Image Generation by Instruction-Learning from Multimodal Patient Journeyscited by 29
  6. 2023Text-to-Image Models for Counterfactual Explanations: a Black-Box Approachcited by 28
  7. 2023Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queriescited by 23
  8. 2024Benchmarking Counterfactual Image Generationcited by 22
  9. 2023From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modelingcited by 21
  10. 2024Counterfactual Image Editingcited by 20
  11. 2023Counterfactual (Non-)identifiability of Learned Structural Causal Modelscited by 17
  12. 2023Latent Diffusion Counterfactual Explanationscited by 17
  13. 2024DiffPO: A causal diffusion model for learning distributions of potential outcomescited by 17
  14. 2023Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelcited by 14
  15. 2023DreaMR: Diffusion-driven Counterfactual Explanation for Functional MRIcited by 14
  16. 2023Finding Counterfactually Optimal Action Sequences in Continuous State Spacescited by 12
  17. 2023Emerging Synergies in Causality and Deep Generative Models: A Surveycited by 10
  18. 2024Counterfactual Generative Modeling with Variational Causal Inferencecited by 10
  19. 2025CF-Seg: Counterfactuals meet Segmentationcited by 10
  20. 2023Deep Backtracking Counterfactuals for Causally Compliant Explanationscited by 8
  21. 2024Generating Counterfactual Trajectories with Latent Diffusion Models for Concept Discoverycited by 8
  22. 2025Diffusion Counterfactual Generation with Semantic Abductioncited by 8
  23. 2023Generator Identification for Linear SDEs with Additive and Multiplicative Noisecited by 7
  24. 2024Zero-Shot Medical Phrase Grounding with Off-the-shelf Diffusion Modelscited by 7
  25. 2023Predictive Coding beyond Correlationscited by 6
  26. 2025DoubleGen: Debiased Generative Modeling of Counterfactualscited by 6
  27. 2022Deep Counterfactual Estimation with Categorical Background Variablescited by 5
  28. 2023Navigating the Structured What-If Spaces: Counterfactual Generation via Structured Diffusioncited by 5
  29. 2025Causally Steered Diffusion for Automated Video Counterfactual Generationcited by 5
  30. 2025Counterfactual Identifiability via Dynamic Optimal Transportcited by 5
  31. 2024Conditional Generative Models are Sufficient to Sample from Any Causal Effect Estimandcited by 4
  32. 2024Language Models as Causal Effect Generatorscited by 4
  33. 2025Counterfactual Probabilistic Diffusion with Expert Modelscited by 4
  34. 2025Causal-Adapter: Taming Text-to-Image Diffusion for Faithful Counterfactual Generationcited by 4
  35. 2023Generating Realistic Counterfactuals for Retinal Fundus and OCT Images using Diffusion Modelscited by 3
  36. 2024Causal Inference with Complex Treatments: A Surveycited by 3
  37. 2025V-CECE: Visual Counterfactual Explanations via Conceptual Editscited by 3
  38. 2025Spatial Deconfounder: Interference-Aware Deconfounding for Spatial Causal Inferencecited by 3

50 most cited of 87 All 87 (JSON)