This paper presents the first comprehensive theoretical explanation, based on computational physical kinetics, for the phenomenon of electrons attaining energies exceeding the amplitude of the applied voltage (in eV units) in a vacuum diode. The proposed theory thoroughly elucidates the existence of so-called “anomalous electrons”, detailing their generation dynamics and underlying mechanisms. Additionally, the work calculates the integral energy spectra of these anomalous electrons in a high-current pulsed vacuum discharge and quantifies their contribution to the total current flow. The main tool used for numerical calculations is the latest meshless method for solving Vlasov-Poisson equation systems, known as the numerical flow iteration method (NuFI). The findings provide critical insights into non-equilibrium electron behaviour under extreme conditions, advancing the understanding of electron transport in vacuum-based high-power devices.