A 2D hot spot diffusion model for describing the superconducting nanowire response to a single photon is presented. Compared to the 1D hot belt model, the 2D hot spot model can capture the initial stage of the hot spot evolution after photon absorption, which is beneficial for achieving a more comprehensive understanding of the origins and underlying physics of the timing jitter in superconducting nanowire-based single-photon detectors. Based on the established 2D diffusion model, the cross-section effect induced by the random radial position of the photon absorption is investigated, which can qualitatively explain the asymmetry and non-Gaussian shape of the probability density function (PDF) distributions of the time delay. Furthermore, the shift of the right half of the PDF distributions with increasing photon wavelength can also be clarified in the framework of the innovative 2D diffusion model. Considering the spatial inhomogeneity along the nanowire, the calculated results of the timing jitter based on the Monte Carlo methods are in good agreement with the experimental observations. The proposed 2D hot spot diffusion model will not only shed light on the origin and influence of the timing jitter but also reveal the working principle of superconducting nanowire devices.