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We study a model of interface dynamics which describes a surface-tension-biased process of simultaneous deposition and evaporation of particles. The control parameter of the model is the average translational velocity (v) of the interface which is determined by the difference between the rates of deposition and evaporation. For v =0 the dynamics is reversible and the two-dimensional problem can be solved exactly by mapping the system onto a kinetic Ising model. For the case of irreversible growth (v&0), we use Monte Carlo methods to calculate the dynamic structure factor, S(k, t), of the surface. We find that S(k, t) obeys dynamic scaling: S(k, t)-k + "f(k't) with g=0 for all v, whereas z =2 for v =0 and z = 2 for v&0. These results suggest that the long-3 wavelength, long-time limit of our interface model can be described by Burgers' equation and, furthermore, that the change in the dynamical exponent z is related to the breaking of time-reversal symmetry which occurs as v becomes nonzero.