# Learning Causally Disentangled Representations via the Principle of Independent Causal Mechanisms

arXiv: https://arxiv.org/abs/2306.01213 · HTML: https://mlsanity.com/paper/2306.01213/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 2 Jun 2023.

## Builds on (most cited first, 29 of 29)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (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)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [DIVA: Domain Invariant Variational Autoencoders](https://mlsanity.com/paper/1905.10427/) (2019)
- [Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness](https://mlsanity.com/paper/1811.00007/) (2018)
- [Learning Independent Causal Mechanisms](https://mlsanity.com/paper/1712.00961/) (2017)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [On Disentangled Representations Learned From Correlated Data](https://mlsanity.com/paper/2006.07886/) (2020)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [Discrete Flows: Invertible Generative Models of Discrete Data](https://mlsanity.com/paper/1905.10347/) (2019)
- [Weakly Supervised Disentangled Generative Causal Representation Learning](https://mlsanity.com/paper/2010.02637/) (2020)
- [Causal Discovery with General Non-Linear Relationships Using Non-Linear ICA](https://mlsanity.com/paper/1904.09096/) (2019)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Capturing Label Characteristics in VAEs](https://mlsanity.com/paper/2006.10102/) (2020)
- [DCI-ES: An Extended Disentanglement Framework with Connections to Identifiability](https://mlsanity.com/paper/2210.00364/) (2022)

## Built on by (most cited first, 14 of 14)

- [Identifiability Guarantees for Causal Disentanglement from Soft Interventions](https://mlsanity.com/paper/2307.06250/) (2023)
- [From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling](https://mlsanity.com/paper/2310.11011/) (2023)
- [Counterfactual Generative Modeling with Variational Causal Inference](https://mlsanity.com/paper/2410.12730/) (2024)
- [CAUSAL3D: A Comprehensive Benchmark for Causal Learning from Visual Data](https://mlsanity.com/paper/2503.04852/) (2025)
- [When Graph Neural Network Meets Causality: Opportunities, Methodologies and An Outlook](https://mlsanity.com/paper/2312.12477/) (2023)
- [Improving Generalization Ability of Robotic Imitation Learning by Resolving Causal Confusion in Observations](https://mlsanity.com/paper/2507.22380/) (2025)
- [Causal-Adapter: Taming Text-to-Image Diffusion for Faithful Counterfactual Generation](https://mlsanity.com/paper/2509.24798/) (2025)
- [Structural Disentanglement of Causal and Correlated Concepts](https://mlsanity.com/paper/2405.16219/) (2024)
- [FlexCausal: Flexible Causal Disentanglement via Structural Flow Priors and Manifold-Aware Interventions](https://mlsanity.com/paper/2601.21567/) (2026)
- [DISCO: Mitigating Bias in Deep Learning with Conditional Distance Correlation](https://mlsanity.com/paper/2506.11653/) (2025)
- [CauCLIP: Bridging the Sim-to-Real Gap in Surgical Video Understanding via Causality-Inspired Vision-Language Modeling](https://mlsanity.com/paper/2602.06619/) (2026)
- [A Systematic Framework for Tabular Data Disentanglement](https://mlsanity.com/paper/2604.07940/) (2026)
- [Leveraging Foundation Models for Causal Generative Modeling](https://mlsanity.com/paper/2605.23861/) (2026)
- [CouCE: A Unified Causal Framework for Debiased Deep Metric Learning](https://mlsanity.com/paper/2606.30365/) (2026)

## Abstract (arXiv)

Learning disentangled causal representations is a challenging problem that has gained significant attention recently due to its implications for extracting meaningful information for downstream tasks. In this work, we define a new notion of causal disentanglement from the perspective of independent causal mechanisms. We propose ICM-VAE, a framework for learning causally disentangled representations supervised by causally related observed labels. We model causal mechanisms using nonlinear learnable flow-based diffeomorphic functions to map noise variables to latent causal variables. Further, to promote the disentanglement of causal factors, we propose a causal disentanglement prior learned from auxiliary labels and the latent causal structure. We theoretically show the identifiability of causal factors and mechanisms up to permutation and elementwise reparameterization. We empirically demonstrate that our framework induces highly disentangled causal factors, improves interventional robustness, and is compatible with counterfactual generation.