# From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling

arXiv: https://arxiv.org/abs/2310.11011 · HTML: https://mlsanity.com/paper/2310.11011/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 83 of its 122 references that are in the map.
- First posted on arXiv 17 Oct 2023.

## Builds on (most cited first, 30 of 83)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Differentially Private Generative Adversarial Network](https://mlsanity.com/paper/1802.06739/) (2018)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)

## Built on by (most cited first, 22 of 22)

- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [Causal Diffusion Autoencoders: Toward Counterfactual Generation via Diffusion Probabilistic Models](https://mlsanity.com/paper/2404.17735/) (2024)
- [Linear Causal Representation Learning from Unknown Multi-node Interventions](https://mlsanity.com/paper/2406.05937/) (2024)
- [Identifiability of Deep Polynomial Neural Networks](https://mlsanity.com/paper/2506.17093/) (2025)
- [Diffusion Counterfactual Generation with Semantic Abduction](https://mlsanity.com/paper/2506.07883/) (2025)
- [DoubleGen: Debiased Generative Modeling of Counterfactuals](https://mlsanity.com/paper/2509.16842/) (2025)
- [Learning Structural Causal Models through Deep Generative Models: Methods, Guarantees, and Challenges](https://mlsanity.com/paper/2405.05025/) (2024)
- [Causal Time Series Generation via Diffusion Models](https://mlsanity.com/paper/2509.20846/) (2025)
- [The Alexander-Hirschowitz theorem for neurovarieties](https://mlsanity.com/paper/2511.19703/) (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)
- [GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomes](https://mlsanity.com/paper/2509.22953/) (2025)
- [Back to the Feature: Explaining Video Classifiers with Video Counterfactual Explanations](https://mlsanity.com/paper/2511.20295/) (2025)
- [Catastrophic Compositional Generation: Why Vanilla Diffusion Models Fail to Extrapolate](https://mlsanity.com/paper/2606.23920/) (2026)
- [Causally Consistent Normalizing Flow](https://mlsanity.com/paper/2412.12401/) (2024)
- [ROPES: Robotic Pose Estimation via Score-Based Causal Representation Learning](https://mlsanity.com/paper/2510.20884/) (2025)
- [Causal Synthetic Data Generation in Recruitment](https://mlsanity.com/paper/2511.16204/) (2025)
- [Identifiable Multimodal Causal Representation Learning under Partial Latent Sharing](https://mlsanity.com/paper/2605.19135/) (2026)
- [Leveraging Foundation Models for Causal Generative Modeling](https://mlsanity.com/paper/2605.23861/) (2026)
- [A Neuroimaging Simulation Framework for Developing and Evaluating Causal AI](https://mlsanity.com/paper/2606.28684/) (2026)
- [Vision: Data-Centric Anchoring for Robust and Interpretable Agentic AI](https://mlsanity.com/paper/2609.08216/) (2026)
- [Causal Representation Learning with Instantaneous and Lagged Relations via Nonstationarity](https://mlsanity.com/paper/2610.03452/) (2026)

## Abstract (arXiv)

Deep generative models have shown tremendous capability in data density estimation and data generation from finite samples. While these models have shown impressive performance by learning correlations among features in the data, some fundamental shortcomings are their lack of explainability, tendency to induce spurious correlations, and poor out-of-distribution extrapolation. To remedy such challenges, recent work has proposed a shift toward causal generative models. Causal models offer several beneficial properties to deep generative models, such as distribution shift robustness, fairness, and interpretability. Structural causal models (SCMs) describe data-generating processes and model complex causal relationships and mechanisms among variables in a system. Thus, SCMs can naturally be combined with deep generative models. We provide a technical survey on causal generative modeling categorized into causal representation learning and controllable counterfactual generation methods. We focus on fundamental theory, methodology, drawbacks, datasets, and metrics. Then, we cover applications of causal generative models in fairness, privacy, out-of-distribution generalization, precision medicine, and biological sciences. Lastly, we discuss open problems and fruitful research directions for future work in the field.