Abstract: Standard mean-based linear models in genome-wide association studies (GWAS) are ill-equipped for the rich, high-dimensional phenotypes increasingly collected in contemporary biobanks. Image-derived phenotypes (IDPs), such as structural brain connectomes, frequently exhibit extreme heavy tails and non-monotone genetic effects. Applying standard GWAS to these non-Gaussian traits causes severe sensitivity to outliers and fails to detect genetic effects manifesting as distributional changes rather than simple mean shifts. To address this, we introduce DiscreteBET, a highly scalable nonparametric framework for testing general genotype–phenotype dependence. Operating at the empirical copula level via rank-based binary expansions, DiscreteBET is strictly invariant to marginal distributions. This natively immunizes the test against extreme outliers without ad-hoc transformations, enabling the detection of complex, non-monotone distributional shifts missed by standard GWAS. In simulations, DiscreteBET demonstrates superior power and stability under nonlinear and heavy-tailed mechanisms. Applied to UK Biobank imaging genetics data, DiscreteBET matches linear GWAS on well-behaved white matter traits but uniquely identifies 710 significant, non-monotone associations within the heavy-tailed structural connectome. These discoveries map to neurodevelopmentally relevant genes invisible to classical linear and rank-based methods, establishing DiscreteBET as a powerful complementary tool in modern statistical genetics. This is joint work with Xinyi Li, Wan Zhang, Zhengwu Zhang and Yize Zhao.