# Structural Disentanglement of Causal and Correlated Concepts

arXiv: https://arxiv.org/abs/2405.16219 · HTML: https://mlsanity.com/paper/2405.16219/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 25 May 2024.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Diffusion Self-Guidance for Controllable Image Generation](https://mlsanity.com/paper/2306.00986/) (2023)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Weakly Supervised Disentangled Generative Causal Representation Learning](https://mlsanity.com/paper/2010.02637/) (2020)
- [Disentangling Factors of Variation Using Few Labels](https://mlsanity.com/paper/1905.01258/) (2019)
- [Learning Latent Subspaces in Variational Autoencoders](https://mlsanity.com/paper/1812.06190/) (2018)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [Regression Transformer: Concurrent sequence regression and generation for molecular language modeling](https://mlsanity.com/paper/2202.01338/) (2022)
- [Amazon-M2: A Multilingual Multi-locale Shopping Session Dataset for Recommendation and Text Generation](https://mlsanity.com/paper/2307.09688/) (2023)
- [Causal Interpretation of Self-Attention in Pre-Trained Transformers](https://mlsanity.com/paper/2310.20307/) (2023)
- [Learning Causally Disentangled Representations via the Principle of Independent Causal Mechanisms](https://mlsanity.com/paper/2306.01213/) (2023)
- [Multi-objective Deep Data Generation with Correlated Property Control](https://mlsanity.com/paper/2210.01796/) (2022)

## Built on by (most cited first, 1 of 1)

- [Controllable Generative Trajectory Prediction via Weak Preference Alignment](https://mlsanity.com/paper/2510.10731/) (2025)

## Abstract (arXiv)

Controllable data generation aims to synthesize data by specifying values for target concepts. Achieving this reliably requires modeling the underlying generative factors and their relationships. In real-world scenarios, these factors exhibit both causal and correlational dependencies, yet most existing methods model only part of this structure. We propose the Causal-Correlation Variational Autoencoder (C2VAE), a unified framework that jointly captures causal and correlational relationships among latent factors. C2VAE organizes the latent space into a structured graph, identifying a set of root causes that govern the generative processes. By optimizing only the root factors relevant to target concepts, the model enables efficient and faithful control. Experiments on synthetic and real-world datasets demonstrate that C2VAE improves generation quality, disentanglement, and intervention fidelity over existing baselines.