Dynamic nuclear polarization via contact with electronic spins has emerged as an attractive route to enhance the sensitivity of nuclear magnetic resonance beyond the traditional limits imposed by magnetic field strength and temperature. Among the various alternative implementations, the use of nitrogen vacancy (NV) centers in diamond-a paramagnetic point defect whose spin can be optically polarized at room temperature-has attracted widespread attention, but applications have been hampered by the need to align the NV axis with the external magnetic field. We overcome this hurdle through the combined use of continuous optical illumination and a microwave sweep over a broad frequency range. As a proof of principle, we demonstrate our approach using powdered diamond with which we attain bulk ¹³C spin polarization in excess of 0.25% under ambient conditions. Remarkably, our technique acts efficiently on diamond crystals of all orientations and polarizes nuclear spins with a sign that depends exclusively on the direction of the microwave sweep. Our work paves the way toward the use of hyperpolarized diamond particles as imaging contrast agents for biosensing and, ultimately, for the hyperpolarization of nuclear spins in arbitrary liquids brought in contact with their surface.