Dynamic light scattering (DLS) is a method used to size nanoscale and submicron particles by measuring their thermal motion (diffusion) in a liquid environment. The measured diffusion coefficients are related to the hydrodynamic particle size via the Stokes-Einstein equation. This paper addresses the application of DLS for the characterization of diluted suspensions of pyrogenic silica, which consist of polydisperse fractal-like aggregates composed of sintered spherical primary particles. Simulations are employed to establish a relationship between the structural properties of the aggregates and their diffusional behavior. Therefore, an algorithm is developed that enables the generation of aggregates with a tunable fractal dimension and an arbitrary number of primary particles. The results provide evidence that the hydrodynamic radii show a different scaling compared to the structural radius of gyration, which is of great relevance for the interpretation of DLS results. In addition, the influence of rotational diffusion has to be accounted for in the measurements.