We introduced a generalized version of the transport of intensity equation from a partially coherent phase-space perspective that relates axial intensity derivative to the transverse divergence of the conditional frequency moment of the Wigner distribution function.This expression provides a powerful analytical tool for the study of phase retrieval and computational imaging under partially coherent illuminations.The correspondence between the Wigner distribution function and the light field in the geometric optics enables extracting phase information from the light field and vice versa for slowly varying specimen under certain simplified illumination conditions.