We show that periodic distributions of gain or losses on the wavelength scale allow managing spatial diffraction of light beams, with no index contrast. It has been recently predicted that such artificial periodic structures, analogous to Photonic Crystals (PhCs), would also hold the novel spatial beam propagation effects reported for PhCs such as subdiffraction propagation, self-collimation, spatial filtering or beam focusing by a lens with flat interfaces. In particular, we consider an ideal periodic 2-dimensional (2D) arrangement of lossy cylinders embedded in air. We analytically show that this loss distribution affects diffraction. Indeed, a significant focusing behind a thin flat-flat crystal slab is observed, following the estimation of anomalous spatial dispersion for specific frequency ranges. Besides, close to the edges of the first Brillouin Zone, the light intensity map of a Gaussian beam exiting the lossy structure exhibits a high transmission windows instead of the transmission stop band expected for PhCs. This results from the strong anisotropic attenuation provided by the loss periodicity. Finally, we also consider a more realistic system with combined modulations of refractive index and losses: a 2D metallic photonic crystal (MPhC). We demonstrate that MPhCs also support selfcollimation and focusing, being such effects associated to zero and negative diffraction respectively. Finally, due to the anisotropic attenuation of light, the structure is also able to spatially filter noisy beams.