# CausalVAE: Structured Causal Disentanglement in Variational Autoencoder

arXiv: https://arxiv.org/abs/2004.08697 · HTML: https://mlsanity.com/paper/2004.08697/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2020.

## Built on by (most cited first, 30 of 48)

- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [A Causal Lens for Controllable Text Generation](https://mlsanity.com/paper/2201.09119/) (2022)
- [Identifying Weight-Variant Latent Causal Models](https://mlsanity.com/paper/2208.14153/) (2022)
- [Causal Concept Graph Models: Beyond Causal Opacity in Deep Learning](https://mlsanity.com/paper/2405.16507/) (2024)
- [Identifiable Latent Polynomial Causal Models Through the Lens of Change](https://mlsanity.com/paper/2310.15580/) (2023)
- [Rethinking Multi-domain Generalization with A General Learning Objective](https://mlsanity.com/paper/2402.18853/) (2024)
- [On Causally Disentangled Representations](https://mlsanity.com/paper/2112.05746/) (2021)
- [Causal Representation Learning from Multimodal Biomedical Observations](https://mlsanity.com/paper/2411.06518/) (2024)
- [Benchmarks, Algorithms, and Metrics for Hierarchical Disentanglement](https://mlsanity.com/paper/2102.05185/) (2021)
- [EchoVideo: Identity-Preserving Human Video Generation by Multimodal Feature Fusion](https://mlsanity.com/paper/2501.13452/) (2025)
- [Intact-VAE: Estimating Treatment Effects under Unobserved Confounding](https://mlsanity.com/paper/2101.06662/) (2021)
- [Matching Learned Causal Effects of Neural Networks with Domain Priors](https://mlsanity.com/paper/2111.12490/) (2021)
- [Deep Backtracking Counterfactuals for Causally Compliant Explanations](https://mlsanity.com/paper/2310.07665/) (2023)
- [Language Agents Meet Causality -- Bridging LLMs and Causal World Models](https://mlsanity.com/paper/2410.19923/) (2024)
- [DeCaFlow: A deconfounding causal generative model](https://mlsanity.com/paper/2503.15114/) (2025)
- [CAUSAL3D: A Comprehensive Benchmark for Causal Learning from Visual Data](https://mlsanity.com/paper/2503.04852/) (2025)
- [Zero-shot Safety Prediction for Autonomous Robots with Foundation World Models](https://mlsanity.com/paper/2404.00462/) (2024)
- [Causally Steered Diffusion for Automated Video Counterfactual Generation](https://mlsanity.com/paper/2506.14404/) (2025)
- [Towards Identifiable Latent Additive Noise Models](https://mlsanity.com/paper/2403.15711/) (2024)
- [Language-Enhanced Latent Representations for Out-of-Distribution Detection in Autonomous Driving](https://mlsanity.com/paper/2405.01691/) (2024)
- [Sequential Representation Learning via Static-Dynamic Conditional Disentanglement](https://mlsanity.com/paper/2408.05599/) (2024)
- [Modular Machine Learning: An Indispensable Path towards New-Generation Large Language Models](https://mlsanity.com/paper/2504.20020/) (2025)
- [Skill Learning via Policy Diversity Yields Identifiable Representations for Reinforcement Learning](https://mlsanity.com/paper/2507.14748/) (2025)
- [CausalVerse: Benchmarking Causal Representation Learning with Configurable High-Fidelity Simulations](https://mlsanity.com/paper/2510.14049/) (2025)
- [De-Biasing Generative Models using Counterfactual Methods](https://mlsanity.com/paper/2207.01575/) (2022)
- [Conditionally Invariant Representation Learning for Disentangling Cellular Heterogeneity](https://mlsanity.com/paper/2307.00558/) (2023)
- [Mixture of Concept Bottleneck Experts](https://mlsanity.com/paper/2602.02886/) (2026)
- [CARE-ECG: Causal Agent-based Reasoning for Explainable and Counterfactual ECG Interpretation](https://mlsanity.com/paper/2604.10420/) (2026)
- [Latent Variable Models for Bayesian Causal Discovery](https://mlsanity.com/paper/2207.05723/) (2022)

## Abstract (arXiv)

Learning disentanglement aims at finding a low dimensional representation which consists of multiple explanatory and generative factors of the observational data. The framework of variational autoencoder (VAE) is commonly used to disentangle independent factors from observations. However, in real scenarios, factors with semantics are not necessarily independent. Instead, there might be an underlying causal structure which renders these factors dependent. We thus propose a new VAE based framework named CausalVAE, which includes a Causal Layer to transform independent exogenous factors into causal endogenous ones that correspond to causally related concepts in data. We further analyze the model identifiabitily, showing that the proposed model learned from observations recovers the true one up to a certain degree by providing supervision signals (e.g. feature labels). Experiments are conducted on various datasets, including synthetic and real word benchmark CelebA. Results show that the causal representations learned by CausalVAE are semantically interpretable, and their causal relationship as a Directed Acyclic Graph (DAG) is identified with good accuracy. Furthermore, we demonstrate that the proposed CausalVAE model is able to generate counterfactual data through "do-operation" to the causal factors.