We propose a novel sensitivity analysis to unobserved confounding in observational studies using copulas and normalizing flows. Using the idea of interventional equivalence of structural causal models, we develop ρρ-GNF (ρρ-graphical normalizing flow), where ρ∈[−1,+1]ρ∈[−1,+1] is a bounded sensitivity parameter. This parameter represents the back-door non-causal association due to unobserved confounding, and which is encoded with a Gaussian copula. In other words, the ρρ-GNF enables scholars to estimate the average causal effect (ACE) as a function of ρρ, while accounting for various assumed strengths of the unobserved confounding. The output of the ρρ-GNF is what we denote as the ρcurveρcurve that provides the bounds for the ACE given an interval of assumed ρρ values. In particular, the ρcurveρcurve enables scholars to identify the confounding strength required to nullify the ACE, similar to other sensitivity analysis methods (e.g., the E-value). Leveraging on experiments from simulated and real-world data, we show the benefits of ρρ-GNF. One benefit is that the ρρ-GNF uses a Gaussian copula to encode the distribution of the unobserved causes, which is commonly used in many applied settings. This distributional assumption produces narrower ACE bounds compared to other popular sensitivity analysis methods.