Generating data with properties of interest by external users while following the right causation among its intrinsic factors is important yet has not been well addressed jointly. This is due to the long-lasting challenge of jointly identifying key latent variables, their causal relations, and their correlation with properties of interest, as well as how to leverage their discoveries toward causally controlled data generation. To address these challenges, we propose a novel deep generative framework called the Correlation-aware Causal Variational Auto-encoder (C2VAE). This framework simultaneously recovers the correlation and causal relationships between properties using disentangled latent vectors. Specifically, causality is captured by learning the causal graph on latent variables through a structural causal model, while correlation is learned via a novel correlation pooling algorithm. Extensive experiments demonstrate C2VAE's ability to accurately recover true causality and correlation, as well as its superiority in controllable data generation compared to baseline models.

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