Laser speckle imaging (LSI) is a fast, noninvasive method to obtain relative particle dynamics in highly light scattering media, such as biological tissue. To make quantitative measurements, we combine LSI with spatial frequency domain imaging, a technique where samples are illuminated with sinusoidal intensity patterns of light that control the characteristic path lengths of photons in the sample. We use both diffusion and radiative transport to predict the speckle contrast of coherent light remitted from turbid media. We validate our technique by measuring known Brownian diffusion coefficients (D(b)) of scattering liquid phantoms. Monte Carlo (MC) simulations of radiative transport were found to provide the most accurate contrast predictions. For polystyrene microspheres of radius 800 nm in water, the expected and fit D(b) using radiative transport were 6.10E-07 and 7.10E-07 mm²/s, respectively. For polystyrene microspheres of radius 1026 nm in water, the expected and fit D(b) were 4.7E-07 and 5.35 mm²/s, respectively. For scattering particles in water-glycerin solutions, the fit fractional changes in D(b) with changes in viscosity were all found to be within 3% of the expected value.