We present results for unforced polymer translocation from simulations using Langevin dynamics in two dimensions (2D) to four dimensions and stochastic rotation dynamics supporting hydrodynamic modes in three dimensions (3D). We compare our results to forced translocation and a simplified model where the polymer escapes from an infinite pore. The simple model shows that the scaling behavior of unforced translocation is independent of the dimension of the side to which the polymer is translocating. We find that, unlike its forced counterpart, unforced translocation dynamics is insensitive to pore design. Hydrodynamics is seen to markedly speed up the unforced translocation process but not to affect the scaling relations. Average mean-squared displacement shows scaling with average transition time in unforced but not in forced translocation. The waiting-time distribution in unforced translocation follows closely Poissonian distribution. Our measured transfer probabilities align well with those obtained from an equilibrium theory in 3D, but somewhat worse in 2D, where a polymer’s relaxation toward equilibrium with respect to its translocation time is slower. Consequently, in stark contrast to forced translocation, unforced translocation is seen to remain close to equilibrium and shows clear universality.