Computations using the joint velocity-scalar probability density function (pdf) method as well as benchmark quality experimental data for swirling and nonswirling hydrogen jet diffusion flames are reported. Previous studies of diffusion flames reported in the literature have been limited to nonswirling flames and have had no detailed velocity data reported in the developing (near-nozzle) region of the flames. The measurements and computations reported herein include velocities (mean and higher moments up to fourth order) and temperature (mean and variance) near the burner exit and downstream locations lip to 26.5 jet diameters. The velocities were measured with a three-component laser-Doppler velocimeter (LDV) and the temperature was measured using coherent anti-Stokes Raman spectroscopy (CARS). The joint pelf method offers significant advantages over conventional methods for computing turbulent reacting flow and the computed results are in good agreement with data. This study serves to present data that can be used far model validation as well as to validate further the joint pdf method.