Experiments have found that diffusion in metabolically active cells is much faster than in dormant cells, especially for large particles. However, the mechanism of this size-dependent diffusion enhancement in living cells is still unclear. In this Letter, we approximate the net effect of metabolic processes as a white-noise active force and simulate a model system of bacterial cytoplasm with a highly polydisperse particle size distribution. We find that diffusion enhancement in active cells relative to dormant cells can be more substantial for large particles. Our simulations agree quantitatively with the experimental data of Escherichia coli, suggesting an autocorrelation function of the active force proportional to the cube of the particle radius. We demonstrate that such a white-noise active force is equivalent to an active force of about 0.57 pN with random orientation. Our work unveils an emergent simplicity of random processes inside living cells.