Electrochemical impedance spectroscopy (EIS) is a technique widely used to characterize electrochemical systems. While EIS is powerful and simple to use, interpreting EIS experiments is not a straightforward task. Equivalent circuits are by far the most commonly used EIS models. However, these circuits models are not unique. To overcome this issue, the research community has shown increasing interest in distributional methods such as the distribution of relaxation times (DRT), and the recently developed distribution of diffusion times (DDT). The DDT method captures the diffusional timescales of electrode particles, and for this reason, is particularly well suited for the study of the EIS response of batteries and supercapacitors. One major assumption of the DDT method is that the electrodes of these devices are thin. This article generalizes the DDT to electrodes of finite thickness, and this analytical model is termed the non-linear distribution of diffusion times (NL-DDT). The NL-DDT is studied using synthetic data and applying it to actual experiments. The study shows that the NL-DDT can recover the diffusional characteristics as well as the physical properties of the electrodes, including the chemical diffusion coefficient and ionic conductivities.