mlsanityData to 7 Oct 2026

Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries

arXiv 2302.00860 ↗First posted 2 Feb 2023stat.ML cs.LG stat.MEcited by 23

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We consider the problem of answering observational, interventional, and counterfactual queries in a causally sufficient setting where only observational data and the causal graph are available. Utilizing the recent developments in diffusion models, we introduce diffusion-based causal models (DCM) to learn causal mechanisms, that generate unique latent encodings. These encodings enable us to directly sample under interventions and perform abduction for counterfactuals. Diffusion models are a natural fit here, since they can encode each node to a latent representation that acts as a proxy for exogenous noise. Our empirical evaluations demonstrate significant improvements over existing state-of-the-art methods for answering causal queries. Furthermore, we provide theoretical results that offer a methodology for analyzing counterfactual estimation in general encoder-decoder models, which could be useful in settings beyond our proposed approach.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 28 of its 46 references that are in the map. First posted on arXiv 2 Feb 2023.

Builds on

28 of 46 references.

Closest ancestors · 6

Same direction, newest first

  1. 2022Diffusion Models for Causal Discovery via Topological Ordering12 Oct
  2. 2022Classifier-Free Diffusion Guidance26 Jul
  3. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  4. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  5. 2020Denoising Diffusion Implicit Models6 Oct
  6. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 22

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  3. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  4. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  5. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 935
  6. 2019Neural Spline Flowscited by 590
  7. 2020Deep Structural Causal Models for Tractable Counterfactual Inferencecited by 210
  8. 2017Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processescited by 156
  9. 2017CausalGAN: Learning Causal Implicit Generative Models with Adversarial Trainingcited by 152
  10. 2020Algorithmic recourse under imperfect causal knowledge: a probabilistic approachcited by 139
  11. 2020Causal Autoregressive Flowscited by 97
  12. 2022Diffusion Causal Models for Counterfactual Estimationcited by 87
10 more
  1. 2020Sample-Efficient Reinforcement Learning via Counterfactual-Based Data Augmentationcited by 57
  2. 2022DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal modelscited by 40
  3. 2021Relating Graph Neural Networks to Structural Causal Modelscited by 39
  4. 2022Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Modelcited by 38
  5. 2018Counterfactual Mean Embeddingscited by 32
  6. 2021Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Modelscited by 22
  7. 2023Counterfactual (Non-)identifiability of Learned Structural Causal Modelscited by 17
  8. 2022Personalized Public Policy Analysis in Social Sciences using Causal-Graphical Normalizing Flowscited by 16
  9. 2020Estimating Causal Effects with the Neural Autoregressive Density Estimatorcited by 8
  10. 2020Causal Inference with Deep Causal Graphscited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 7; 2024: 1; 2025: 7; 2026: 8.

23 papers.

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  1. 2023Causal normalizing flows: from theory to practicecited by 49
  2. 2023From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modelingcited by 21
  3. 2023Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelcited by 14
  4. 2023Predictive Coding beyond Correlationscited by 6
  5. 2025DoubleGen: Debiased Generative Modeling of Counterfactualscited by 6
  6. 2025Counterfactual Probabilistic Diffusion with Expert Modelscited by 4
  7. 2025Causal-Adapter: Taming Text-to-Image Diffusion for Faithful Counterfactual Generationcited by 4
  8. 2025Improving the Generation and Evaluation of Synthetic Data for Downstream Medical Causal Inferencecited by 4
  9. 2023Reinterpreting causal discovery as the task of predicting unobserved joint statisticscited by 3
  10. 2023Diffusion Model in Causal Inference with Unmeasured Confounderscited by 3
  11. 2024Causal Bayesian Optimization via Exogenous Distribution Learningcited by 3
  12. 2025DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Seriescited by 3
11 more
  1. 2026FoundCause: Causal Discovery with Latent Confounders from Observational Datacited by 3
  2. 2023Advancing Counterfactual Inference through Nonlinear Quantile Regressioncited by 1
  3. 2026Joint Treatment Effect Estimation from Incomplete Healthcare Data: Temporal Causal Normalizing Flows with LLM-driven Evolutionary MNAR Imputationcited by 1
  4. 2025Learning Counterfactually Fair Models via Improved Generation with Neural Causal Modelscited by 0
  5. 2025Partially Functional Dynamic Backdoor Diffusion-based Causal Modelcited by 0
  6. 2026Uncertainty-aware Causal Decision Making via Effect Bound Decompositioncited by 0
  7. 2026JANUS: Structured Bidirectional Generation for Guaranteed Constraints and Analytical Uncertaintycited by 0
  8. 2026Kolmogorov-Arnold causal generative modelscited by 0
  9. 2026Causality-Encoded Diffusion Models for Interventional Sampling and Edge Inferencecited by 0
  10. 2026CAFE: Counterfactual Prediction via Fast Posterior Estimationcited by 0
  11. 2026Learning Causal Normalizing Flows from Incomplete Data via Observed-Data Likelihoodcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024DiffusionCounterfactuals: Inferring High-dimensional Counterfactuals with Guidance of Causal Representations
  2. 2025The Causal Round Trip: Generating Authentic Counterfactuals by Eliminating Information Loss
  3. 2024Causal Diffusion Autoencoders: Toward Counterfactual Generation via Diffusion Probabilistic Models
  4. 2025DifCluE: Generating Counterfactual Explanations with Diffusion Autoencoders and modal clustering
  5. 2024Ablation Based Counterfactuals
  6. 2024Counterfactual Causal Inference in Natural Language with Large Language Models
  7. 2026LLM Explainability with Counterfactual Chains and Causal Graphs
  8. 2025Causal Cartographer: From Mapping to Reasoning Over Counterfactual Worlds