Generative models can be applied in diverse domains, from natural language processing to image synthesis. However, despite this success, a key challenge that remains is the ability to control the generated content. We argue that adequate control of the generation process requires a data representation that allows users to access and efficiently manipulate the semantic factors shaping the data distribution. This work advocates for the adoption of succinct, informative, and interpretable representations, quantified using information-theoretic principles. Through extensive experiments, we demonstrate the efficacy of our proposed framework both qualitatively and quantitatively. Our work contributes to the ongoing quest to enhance both controllability and interpretability in the generation process. Code available at github.com/ArmandCom/InCoDe.