We analyze theoretically and investigate experimentally the transfer of phase to intensity power spectra of spatial frequencies through free-space Fresnel diffraction. Depending on lambda z (where lambda is the wavelength and z is the free-space propagation distance) and the phase-modulation strength S, we demonstrate that for multiscale and broad phase spectra critical behavior transmutes a quasilinear to a nonlinear diffractogram except for low frequencies. On the contrary, a single-scale and broad phase spectrum induces a critical transition in the diffractogram at low frequencies. In both cases, identifying critical behavior encoded in the intensity power spectra is of fundamental interest because it exhibits the limits of perturbative power counting but also guides resolution and contrast optimization in propagation-based, single-distance, phase-contrast imaging, given certain dose and coherence constraints.