# Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries

arXiv: https://arxiv.org/abs/2302.00860 · HTML: https://mlsanity.com/paper/2302.00860/

## Key facts

- Cited by 24 papers in the map (data through 14 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.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [Sample-Efficient Reinforcement Learning via Counterfactual-Based Data Augmentation](https://mlsanity.com/paper/2012.09092/) (2020)
- [Relating Graph Neural Networks to Structural Causal Models](https://mlsanity.com/paper/2109.04173/) (2021)
- [DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal models](https://mlsanity.com/paper/2206.06821/) (2022)
- [Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Model](https://mlsanity.com/paper/2205.13085/) (2022)
- [Counterfactual Mean Embeddings](https://mlsanity.com/paper/1805.08845/) (2018)
- [Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Models](https://mlsanity.com/paper/2102.10440/) (2021)
- [Counterfactual (Non-)identifiability of Learned Structural Causal Models](https://mlsanity.com/paper/2301.09031/) (2023)
- [Personalized Public Policy Analysis in Social Sciences using Causal-Graphical Normalizing Flows](https://mlsanity.com/paper/2202.03281/) (2022)
- [Estimating Causal Effects with the Neural Autoregressive Density Estimator](https://mlsanity.com/paper/2008.07283/) (2020)
- [Causal Inference with Deep Causal Graphs](https://mlsanity.com/paper/2006.08380/) (2020)

## Built on by (most cited first, 24 of 24)

- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling](https://mlsanity.com/paper/2310.11011/) (2023)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [DoubleGen: Debiased Generative Modeling of Counterfactuals](https://mlsanity.com/paper/2509.16842/) (2025)
- [Predictive Coding beyond Correlations](https://mlsanity.com/paper/2306.15479/) (2023)
- [Reinterpreting causal discovery as the task of predicting unobserved joint statistics](https://mlsanity.com/paper/2305.06894/) (2023)
- [Counterfactual Probabilistic Diffusion with Expert Models](https://mlsanity.com/paper/2508.13355/) (2025)
- [Causal-Adapter: Taming Text-to-Image Diffusion for Faithful Counterfactual Generation](https://mlsanity.com/paper/2509.24798/) (2025)
- [Improving the Generation and Evaluation of Synthetic Data for Downstream Medical Causal Inference](https://mlsanity.com/paper/2510.18768/) (2025)
- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [Diffusion Model in Causal Inference with Unmeasured Confounders](https://mlsanity.com/paper/2308.03669/) (2023)
- [Causal Bayesian Optimization via Exogenous Distribution Learning](https://mlsanity.com/paper/2402.02277/) (2024)
- [TabFORGE: A Tabular Foundation Model for Generative Modelling](https://mlsanity.com/paper/2605.09424/) (2026)
- [FoundCause: Causal Discovery with Latent Confounders from Observational Data](https://mlsanity.com/paper/2606.17516/) (2026)
- [Advancing Counterfactual Inference through Nonlinear Quantile Regression](https://mlsanity.com/paper/2306.05751/) (2023)
- [Joint Treatment Effect Estimation from Incomplete Healthcare Data: Temporal Causal Normalizing Flows with LLM-driven Evolutionary MNAR Imputation](https://mlsanity.com/paper/2605.05125/) (2026)
- [Learning Counterfactually Fair Models via Improved Generation with Neural Causal Models](https://mlsanity.com/paper/2502.12796/) (2025)
- [Partially Functional Dynamic Backdoor Diffusion-based Causal Model](https://mlsanity.com/paper/2509.00472/) (2025)
- [Uncertainty-aware Causal Decision Making via Effect Bound Decomposition](https://mlsanity.com/paper/2601.22736/) (2026)
- [JANUS: Structured Bidirectional Generation for Guaranteed Constraints and Analytical Uncertainty](https://mlsanity.com/paper/2603.03748/) (2026)
- [Kolmogorov-Arnold causal generative models](https://mlsanity.com/paper/2603.20184/) (2026)
- [Causality-Encoded Diffusion Models for Interventional Sampling and Edge Inference](https://mlsanity.com/paper/2604.21843/) (2026)
- [CAFE: Counterfactual Prediction via Fast Posterior Estimation](https://mlsanity.com/paper/2609.32167/) (2026)
- [Learning Causal Normalizing Flows from Incomplete Data via Observed-Data Likelihood](https://mlsanity.com/paper/2609.37664/) (2026)

## 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.