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 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
that utilizes the known causal structure to encourage learning a causally
factorized distribution in the latent space. Under relatively mild conditions,
we provide theoretical results showing 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