The absence of photobleaching, blinking, and saturation combined with a high contrast provides unique advantages of higher-harmonic generating nanoparticles over fluorescent probes, allowing for prolonged correlation spectroscopy studies. We apply the coherent intensity fluctuation model to study the mobility of second harmonic generating nanoparticles. A concise protocol is presented for quantifying the diffusion coefficient from a single spectroscopy measurement without the need for separate point-spread-function calibrations. The technique's applicability is illustrated on nominally 56 nm LiNbO3 nanoparticles. We perform label-free raster image correlation spectroscopy imaging in aqueous suspension and spatiotemporal image correlation spectroscopy in A549 human lung carcinoma cells. In good agreement with the expected theoretical result, the measured diffusion coefficient in water at room temperature is (7.5 ± 0.3) µm^2/s. The diffusion coefficient in the cells is more than 10^3 times lower, and heterogeneous, with an average of (3.7 ± 1.5) x 10^(-3) µm^2/s.