Estimating three-dimensional complex permittivity of a sample from the intensity recorded at the image plane of a microscope for various angles of illumination, as in optical Fourier ptychography microscopy, permits one to avoid the interferometric measurements of classical tomographic diffraction microscopes (TDMs). In this work, we present a general inversion scheme for processing intensities that can be applied to any microscope configuration (transmission or reflection, low or high numerical aperture), scattering regime (single or multiple scattering), or sample-holder geometries (with or without substrate). The inversion procedure is tested on a wide variety of synthetic experiments, and the reconstructions are compared to that of TDMs. In most cases, phaseless data yield the same result as complex data, thus paving the way toward a drastic simplification of TDM implementation.