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The control of polarization, an essential property of light, is of wide scientific and technological interest. Polarizer is an indispensable optical element for direct polarization generations. Except common linear and circular polarizations, however, arbitrary polarization generation heavily resorts to bulky optical components by cascading linear polarizers and waveplates. Here, we present a general strategy for designing all-in-one full Poincaré sphere polarizers based on perfect arbitrary polarization conversion dichroism, and realize it in a monolayer all-dielectric metasurface. It allows preferential transmission and conversion of one polarization state locating at an arbitrary position of the Poincaré sphere to its handedness-flipped state, while completely blocking its orthogonal state. In contrast to previous work with limited flexibility to only linear or circular polarizations, our method manifests perfect dichroism close to 100% in theory and exceeding 90% in experiments for arbitrary polarization states. Leveraging this tantalizing dichroism, our demonstration of monolithic full Poincaré sphere polarization generators directly from unpolarized light can enormously extend the scope of meta-optics and dramatically push the state-of-the-art nanophotonic devices.