# Conditional Generative Models are Sufficient to Sample from Any Causal Effect Estimand

arXiv: https://arxiv.org/abs/2402.07419 · HTML: https://mlsanity.com/paper/2402.07419/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 70 references that are in the map.
- First posted on arXiv 12 Feb 2024.

## Builds on (most cited first, 30 of 35)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (2017)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Making the Most of Text Semantics to Improve Biomedical Vision--Language Processing](https://mlsanity.com/paper/2204.09817/) (2022)
- [COVID-Net: A Tailored Deep Convolutional Neural Network Design for Detection of COVID-19 Cases from Chest X-Ray Images](https://mlsanity.com/paper/2003.09871/) (2020)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equations](https://mlsanity.com/paper/2207.06635/) (2022)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Explaining Classifiers with Causal Concept Effect (CaCE)](https://mlsanity.com/paper/1907.07165/) (2019)
- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [RoentGen: Vision-Language Foundation Model for Chest X-ray Generation](https://mlsanity.com/paper/2211.12737/) (2022)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [Morpho-MNIST: Quantitative Assessment and Diagnostics for Representation Learning](https://mlsanity.com/paper/1809.10780/) (2018)
- [A Causal View on Robustness of Neural Networks](https://mlsanity.com/paper/2005.01095/) (2020)
- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [Measuring axiomatic soundness of counterfactual image models](https://mlsanity.com/paper/2303.01274/) (2023)
- [Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Models](https://mlsanity.com/paper/2102.10440/) (2021)
- [An Adaptive Kernel Approach to Federated Learning of Heterogeneous Causal Effects](https://mlsanity.com/paper/2301.00346/) (2023)
- [Partial Identification of Treatment Effects with Implicit Generative Models](https://mlsanity.com/paper/2210.08139/) (2022)
- [Causal Identification under Markov Equivalence](https://mlsanity.com/paper/1812.06209/) (2018)
- [Compositional Probabilistic and Causal Inference using Tractable Circuit Models](https://mlsanity.com/paper/2304.08278/) (2023)

## Built on by (most cited first, 4 of 4)

- [Diffusion Counterfactual Generation with Semantic Abduction](https://mlsanity.com/paper/2506.07883/) (2025)
- [Uncertainty-aware Causal Decision Making via Effect Bound Decomposition](https://mlsanity.com/paper/2601.22736/) (2026)
- [Out of Context: Reliability in Multimodal Anomaly Detection Requires Contextual Inference](https://mlsanity.com/paper/2604.13252/) (2026)
- [Counterfactual identifiability beyond global monotonicity: non-monotone triangular structural causal models](https://mlsanity.com/paper/2605.04413/) (2026)

## Abstract (arXiv)

Causal inference from observational data plays critical role in many applications in trustworthy machine learning. While sound and complete algorithms exist to compute causal effects, many of them assume access to conditional likelihoods, which is difficult to estimate for high-dimensional (particularly image) data. Researchers have alleviated this issue by simulating causal relations with neural models. However, when we have high-dimensional variables in the causal graph along with some unobserved confounders, no existing work can effectively sample from the un/conditional interventional distributions. In this work, we show how to sample from any identifiable interventional distribution given an arbitrary causal graph through a sequence of push-forward computations of conditional generative models, such as diffusion models. Our proposed algorithm follows the recursive steps of the existing likelihood-based identification algorithms to train a set of feed-forward models, and connect them in a specific way to sample from the desired distribution. We conduct experiments on a Colored MNIST dataset having both the treatment (X) and the target variables (Y) as images and sample from P(y|do(x)). Our algorithm also enables us to conduct a causal analysis to evaluate spurious correlations among input features of generative models pre-trained on the CelebA dataset. Finally, we generate high-dimensional interventional samples from the MIMIC-CXR dataset involving text and image variables.