Using fluorescence correlation spectroscopy (FCS) to distinguish between different types of diffusion processes is often a perilous undertaking, as the analysis of the resulting autocorrelation data is model-dependant. Two recently introduced strategies, however, can help move towards a model-independent interpretation of FCS experiments: 1) the obtention of correlation data at different length-scales and 2) its inversion to retrieve the mean-squared displacement associated with the process under study. We use computer simulations to examine the signature of several biologically relevant diffusion processes (simple diffusion, continuous-time random walk, caged diffusion, obstructed diffusion, two-state diffusion and diffusing diffusivity) in variable-lengthscale FCS. We show that, when used in concert, lengthscale variation and data inversion permit to identify non-Gaussian processes and, regardless of Gaussianity, to retrieve their mean-squared displacement over several orders of magnitude in time. This makes unbiased discrimination between different classes of diffusion models possible.