A 2D hot spot diffusion model for describing the superconducting nanowire response to single photon is presented. We develop the 1D hot belt model to 2D hot spot model and can capture the initial stage of the hot spot evolution after photon absorption, this is helpful to comprehensive understand the origins and underlying physics of time jitter in superconducting nanowire-based single-photon detectors. Furthermore, the developed model can qualitatively explain the asymmetry and photon wavelength dependent probability density function (PDF) of the delay time. We find that the left and right half of the PDF distributions respective exhibit the Gauss and non-Gauss shape as increasing the excitation wavelength or decreasing the bias current, and the origins are discussed and analyzed in the framework of newly developed 2D model. The proposed 2D hot spot diffusion model will not only sheds light on the origin and influence of the timing jitter but will also reveal the work principle of the superconducting nanowire devices.