High-pressure and variable temperature single crystal synchrotron X-ray measurements combined with first-principles based molecular dynamics simulations study diffuse scattering in the relaxor ferroelectric system PSN (PbSc 1/2 Nb 1/2 O3). Constant temperature experiments show pressure induced transition to the relaxor phase at different temperatures characterized by butterfly and rod shaped diffuse scattering around the {h00} and {hh0} Bragg spots, respectively. The simulations reproduce the observed diffuse scattering features as well as their pressure-temperature behavior, and show that they arise from polarization correlations between chemically-ordered regions, which in previous simulations were shown to behave as polar nanoregions. Simulations also exhibit radial diffuse scattering (elongated towards and away from Q=(000)), that persists even in the paraelectric phase, consistent with previous neutron experiments on (PbMg 1/3 Nb 2/3 O3) (PMN).Single crystal relaxors have huge electromechanical coupling, and show much promise for ultrasonic transducer applications [1]. They have broad frequency and temperature dependent dielectric maxima, which in the special case of relaxor-ferroelectrics [2,3] drops to a much lower value below the ferroelectric transition temperature (T F E ). The origin of the relaxor phase has been a topic of intense research for over a decade. From refractive index measurements, Burns et al. [4] suggested that formation of polar clusters below a characteristic temperature, now called the Burns temperature (T d ) [4], gives rise to dielectric dispersion, which was confirmed experimentally [5]. These clusters thought to be a few nanometers in size are called polar nanoregions (PNRs).Recent X-ray and neutron experiments show characteristic shapes of diffuse scattering in the relaxor phase of several lead based relaxors [6,7,8,9] absent in their paraelectric or ferroelectric phases. The main observed feature is anisotropic diffuse scattering around the Bragg peaks along <110> directions. The ferroelectric phase shows weak streaks similar to BaTiO 3 and KNbO 3 , but rotated by 45-degrees. The paraelectric phase only shows radial diffuse scattering.Several hypotheses previously advanced to explain the characteristic shapes [6,10,11,12], invoke some type of artificial anisotropic features such as anisotropic strain, correlated atomic shifts, or domain boundaries to generate the experimentally observed anisotropic diffuse scattering features. Fitting the shapes of diffuse scattering features is not sufficient to uniquely determine the nature of the microstructural feature that give rise to them. Incorporating realistic polarization fluctuations via first-principles derived models provide a basis for clarifying the nature of the PNR in relaxors and experimental diffuse scattering observations provide a critical test for any theoretical model. In this Letter, we clarify the microstructural origin of diffuse scattering features in the relaxor-and the paraelectric-phases of PSN, and related materi...