Discovering causal relationships from observational data is an essential yet challenging task. While significant progress has been made for pairwise causal discovery with continuous data, methods tailored specifically to categorical data remain limited. In this paper, we introduce a novel geometric complexity-based approach that addresses this gap by effectively approximating transmission lengths of categorical variables. Inspired by the Additive Noise Model principle, our approach compares encoding lengths for each potential causal direction—adhering to Occam’s razor, the direction providing a simpler encoding is inferred as causal. Additionally, we propose a generalized non-functional variant that relaxes the independent noise assumption, searching instead for the most compressible conditional distribution. Experiments on synthetic, benchmark, and real-world datasets demonstrate that our method consistently matches or surpasses state-of-the-art alternatives.