By varying the degree of correlation in stealthy hyperuniform (SHU) materials, the continuous evolution from uncorrelated disorder to periodic media is possible and allows us, as such, to study the fate of the bimodal distribution, the characteristic of a diffusive transport. Considering the wave transport through a SHU distribution of a given number of scatterers and at a given frequency, the transition from a diffusive to a transparent medium is clearly observed only below the Bragg frequency. This transition is characterized by a threshold value of the stealthiness at the vicinity of which the material abruptly changes from diffusive to transparent. In contrast, no such clear transition is observed at or above the Bragg frequency and, surprisingly, a seemingly bimodal distribution of the transmission eigenvalues still characterizes the SHU materials, even when strongly correlated.