  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.
