Dynamic nuclear polarization (DNP) is a promising strategy for generating a significantly increased non-thermal spin polarization in nuclear magnetic resonance (NMR) applications thereby circumventing the need for strong magnetic fields. Although much explored in recent experiments, a detailed theoretical understanding of the precise mechanism behind DNP is so far lacking. We address this issue by theoretically investigating solid effect DNP in a system where a single electron is coupled to an ensemble of interacting nuclei and which can be microscopically modelled by a quantum master equation. By deriving effective equations of motion that govern the polarization dynamics we show analytically that DNP can be understood as kinetically constrained spin diffusion. On the one hand this approach provides analytical insights into the mechanism and timescales underlying DNP. On the other hand it permits the numerical study of large ensembles which are typically intractable from the perspective of a quantum master equation. This paves the way for a detailed exploration of DNP dynamics which might form the basis for future NMR applications. ; Comment: 13 pages, 5 figures