A novel propagator approach for NMR signal attenuation due to anisotropic diffusion is proposed, with consideration of the loss of spin phase memory during random motion. This method is applied to explicitly investigate free diffusion, restricted diffusion between two parallel plates, and diffusions under different nonlinear gradients, including an n-order nonlinear field and gradient with a cosine distribution. The method provides an intuitive physical picture and simplifies the treatment with the effects of finite-width gradient pulses in restricted diffusion and with nonlinear gradients. Theoretical results are in good agreement with those of previous reports.