We study dye regeneration dynamics in dye-sensitized solar cells using extensive kinetic Monte Carlo simulations of transient absorption experiments. Using the long-range charge transfer model as the regeneration mechanisms, the dependency of the regeneration kinetics on concentration and diffusion speed of the reducing species is investigated. At initial times, the kinetics is exponential and mainly determined by the intrinsic regeneration rate coefficient, irrespective of the diffusion coefficient. At later times, however, depending on the concentration of the reducing species, the diffusion starts to play a role in the regeneration process, leading to a stretched tail. We discuss that this concentration dependence cannot be described by the approaches based on the Smoluchowski model. We also compare different methods used in experiments for estimating the rate coefficient from the decay curve, and it is shown that different methods may lead to different conclusions about the regeneration mechanisms. Th...