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

Abstract: 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.