  The three dimensional distribution of the X-ray diffuse scattering intensity
of BaTiO$_3$ has been recorded in a synchrotron experiment and simultaneously
computed using molecular dynamics simulations of a shell-model. Together these
have allowed the details of the disorder in paraelectric BaTiO$_3$ to be
clarified. The narrow sheets of diffuse scattering, related to the famous
anisotropic longitudinal correlations of Ti ions, are shown to be caused
entirely by the overdamped anharmonic soft phonon branch. This finding
demonstrates that the occurrence of narrow sheets of diffuse scattering agrees
with a displacive picture of the cubic phase of this textbook ferroelectric
material.
