We report the first simulations of nonsolvent-induced phase separation (NIPS) that predict membrane microstructures with graded asymmetric pore size distribution. In NIPS, a polymer solution film is immersed in a nonsolvent bath, enriching the film in nonsolvent, and leading to phase separation that forms a solid polymer-rich membrane matrix and polymer-poor membrane pores. We demonstrate how mass-transfer-induced spinodal decomposition, thermal fluctuations, and glass-transition dynamicsimplemented with mobility contrast between the polymer-rich and polymer-poor phasesare essential to the formation of asymmetric membrane microstructures. Specifically, we show that the competition between the propagation of the phase-separation and glass-transition fronts determines the degree of pore-size asymmetry. We also explore the sensitivity of these microstructures to the initial film composition, and compare their formation in 2D and 3D.