Quantum effects on diffusion in liquid para-hydrogen at temperatures of T = 17 and 25 K and saturated vapor pressure is studied by calculating the diffusion coefficient from the standard Green-Kubo formula, using both the ordinary velocity correlation function (CF) and its Kubo-transformed counterpart. All CFs are calculated with a recently proposed linearized path integral expression for general CFs, using an approximate Wigner transformed Boltzmann operator based on Feynman-Kleinert variational path integral theory. Also, the ability of the approximate Wigner transform to predict the radial distribution function and kinetic energy of the liquid is investigated. The conclusions are as follows: (i) The predicted structure of liquid parahydrogen is in excellent agreement with accurate path integral Monte Carlo calculations at both temperatures. (ii) The calculated liquid kinetic energy is in very good agreement with the accurate value at T = 25 K but deviates somewhat from the accurate value at T = 17 K. (iii) The diffusion coefficients based on the Kubo-transformed CF are in very good agreement with experiment, at both temperatures, whereas results from the ordinary velocity CF are not accurate at T = 17 K. The reason for the better performance of the Kubo CF approach is attributed to the latter's robustness toward errors in the approximate Boltzmann operator Wigner transform. The kinetic energy derived from the Kubo-transformed CFs is in excellent agreement with accurate values at both temperatures.