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In this paper, we report on results from a computational investigation of nanosecond pulsed discharges in air of negative polarity using a two-dimensional fluid and fluid-Monte Carlo simulations. The computational parameters and conditions are taken from an experiment. The discharge is initiated near the cathode having a small radius of curvature and propagates towards the flat anode. The simulations are done in atmospheric pressure air with a nanosecond pulse of 120 kV amplitude in a 12 mm gap with a sharp cathode. The essential difference between discharges initiated by low- and high-energy beams of electrons originating in the vicinity of the cathode was observed. The beam of electrons with the initial energy of 20 keV was shown to result in a diffuse discharge, while the 20 eV beam had a negligible influence on the discharge evolution. By analyzing the experimental and computational results, we conclude that a diffuse discharge is formed due to fast electrons without any assumptions on the critical role of the runaway electrons. More study is required to explore the intermediate range of energies and investigate the transition to the diffuse mode of the discharge.