# FlexCausal: Flexible Causal Disentanglement via Structural Flow Priors and Manifold-Aware Interventions

arXiv: https://arxiv.org/abs/2601.21567 · HTML: https://mlsanity.com/paper/2601.21567/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [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)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)
- [Weakly Supervised Disentangled Generative Causal Representation Learning](https://mlsanity.com/paper/2010.02637/) (2020)
- [Causal Representation Learning from Multiple Distributions: A General Setting](https://mlsanity.com/paper/2402.05052/) (2024)
- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [Equitability, mutual information, and the maximal information coefficient](https://mlsanity.com/paper/1301.7745/) (2013)
- [Causal Diffusion Autoencoders: Toward Counterfactual Generation via Diffusion Probabilistic Models](https://mlsanity.com/paper/2404.17735/) (2024)
- [Learning Causally Disentangled Representations via the Principle of Independent Causal Mechanisms](https://mlsanity.com/paper/2306.01213/) (2023)
- [C-Disentanglement: Discovering Causally-Independent Generative Factors under an Inductive Bias of Confounder](https://mlsanity.com/paper/2310.17325/) (2023)
- [Causal Flow-based Variational Auto-Encoder for Disentangled Causal Representation Learning](https://mlsanity.com/paper/2304.09010/) (2023)

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

- [Scalable Minimal-Change Learning for Controllable Image Editing](https://mlsanity.com/paper/2610.06021/) (2026)

## Abstract (arXiv)

Causal Disentangled Representation Learning(CDRL) aims to learn and disentangle low dimensional representations and their underlying causal structure from observations. However, existing disentanglement methods rely on a standard mean-field approximation with a diagonal posterior covariance, which decorrelates all latent dimensions. Additionally, these methods often assume isotropic Gaussian priors for exogenous noise, failing to capture the complex, non-Gaussian statistical properties prevalent in real-world causal factors. Therefore, we propose FlexCausal, a novel CDRL framework based on a block-diagonal covariance VAE. FlexCausal utilizes a Factorized Flow-based Prior to realistically model the complex densities of exogenous noise, effectively decoupling the learning of causal mechanisms from distributional statistics. By integrating supervised alignment objectives with counterfactual consistency constraints, our framework ensures a precise structural correspondence between the learned latent subspaces and the ground-truth causal relations. Finally, we introduce a manifold-aware relative intervention strategy to ensure high-fidelity generation. Experimental results on both synthetic and real-world datasets demonstrate that FlexCausal significantly outperforms other methods.