We propose a theory of the Overhauser effect in the context of electron spin resonance (ESR), including nuclear spin diffusion and spectral diffusion. It is shown that these processes can be observed at low temperatures and strong magnetic fields. These conditions increase the observed cross-transition times and necessitate accounting for slower diffusion mechanisms. We applied the developed theory to explain the mechanism of nuclear spin polarization of individual ²⁹Si atoms in a Si:As crystal under ESR conditions. An approach is proposed for estimating the nuclear spin diffusion coefficient, the spectral diffusion parameters and the nuclear spin relaxation time. We show that an accurate description of the dynamic nuclear polarization of ²⁹Si requires incorporating the frozen core model and estimate the nuclear spin diffusion coefficient inside the frozen core, which was previously assumed to be zero.