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Dephasing and relaxation of the nuclear spins coupled to the nitrogen-vacancy (NV) center during optical initialization and readout is an important issue for various applications of this hybrid quantum register. Here we present both an analytical description and a numerical simulation for this process, which agree reasonably with the experimental measurements. For an NV center under cyclic optical transition, our analytical formulas not only provide a clear physical picture, but also allow control of the nuclear spin dissipation by tuning an external magnetic field. For more general optical pumping, our analytical formulas reveal a significant contribution to the nuclear spin dissipation due to electron random hopping into/out of the m  = 0 (or $m=\pm 1$ ) subspace. This contribution is not suppressed, even under saturated optical pumping and/or vanishing magnetic field, thus providing a possible solution to the puzzling observation of nuclear spin dephasing in zero perpendicular magnetic field Dutt et al (2007 Science   http://dx.doi.org/10.1126/science.1139831 316 http://dx.doi.org/10.1126/science.1139831 ). It also implies that enhancing the degree of optical spin polarization of the nitrogen-vacancy center can reduce the effect of optically induced nuclear spin dissipation.