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Complex multiscale flows associated with instabilities and turbulence are commonly induced under high-energy density (HED) conditions, but accurate measurement of their transport properties has been challenging. x-ray photon correlation spectroscopy (XPCS) with coherent xx-ray sources can, in principle, probe material dynamics to infer transport properties using time autocorrelation of density fluctuations. Here we develop a theoretical framework for utilizing XPCS to study material diffusivity in multiscale flows. We extend single-scale shear flow theories to broadband flows using a multiscale analysis that captures shear and diffusion dynamics. Our theory is validated with simulated XPCS for Brownian particles advected in multiscale flows. We demonstrate the versatility of the method over several orders of magnitude in timescale using sequential-pulse XPCS, single-pulse xx-ray speckle visibility spectroscopy (XSVS), and double-pulse XSVS. Published by the American Physical Society2025