Abstract: Counterfactual image editing is an important problem in generative AI. The current literature on the topic focuses primarily on changing individual features while being silent about the causal relationships between these features present in the real world. In this paper, we first formalize this task through causal language, modeling the causal relationships between latent generative factors and images through a special type of causal model called augmented structural causal models (ASCMs). Second, we show two fundamental impossibility results in this context: (1) counterfactual editing is impossible from i.i.d. image samples and their corresponding labels alone; (2) also, even when the causal relationships between latent generative factors and images are available, no guarantees regarding the output of the generative model can be provided. Third, we propose a relaxation over this hard problem aiming to approximate the non-identifiable target counterfactual distributions while still preserving features the users care about and that are causally consistent with the true generative model, which we call $\textbf{Ctf-consistent estimators}$. Finally, we develop an efficient algorithm to generate counterfactual image samples leveraging neural causal models.