This paper addresses the problem of causal representation learning from multiple distributions, focusing on a general, nonparametric setting without assuming hard interventions or parametric models. The authors aim to recover latent causal variables and their causal relations, which are represented by a graph \(\mathcal{G}_Z\). They show that under sparsity constraints on the recovered graph and suitable change conditions on causal influences, the moralized graph of the underlying directed acyclic graph (DAG) can be recovered, and the latent variables and their relations are related to the true causal model in a specific, nontrivial way. The paper provides theoretical results and experimental validation to support these findings, demonstrating that most latent variables can be recovered up to component-wise transformations. The contributions include identifying the necessary conditions for recovering the latent Markov network and the latent causal DAG, and proposing practical implementations using variational autoencoders (VAEs) and normalizing flows. The results highlight the importance of sparsity constraints and sufficient change conditions in causal representation learning, providing insights into the identifiability of latent causal variables and structures in complex, real-world scenarios.This paper addresses the problem of causal representation learning from multiple distributions, focusing on a general, nonparametric setting without assuming hard interventions or parametric models. The authors aim to recover latent causal variables and their causal relations, which are represented by a graph \(\mathcal{G}_Z\). They show that under sparsity constraints on the recovered graph and suitable change conditions on causal influences, the moralized graph of the underlying directed acyclic graph (DAG) can be recovered, and the latent variables and their relations are related to the true causal model in a specific, nontrivial way. The paper provides theoretical results and experimental validation to support these findings, demonstrating that most latent variables can be recovered up to component-wise transformations. The contributions include identifying the necessary conditions for recovering the latent Markov network and the latent causal DAG, and proposing practical implementations using variational autoencoders (VAEs) and normalizing flows. The results highlight the importance of sparsity constraints and sufficient change conditions in causal representation learning, providing insights into the identifiability of latent causal variables and structures in complex, real-world scenarios.