A seamless chip-to-world photonic interface enables broad advancements in optical ranging, display, communication, computation and quantum information science. The ideal solution enables two-dimensional scanning of a diffraction-limited beam from anywhere on a photonic integrated circuit to a large number of resolvable spots. Current beam-scanning technologies are limited by a fundamental trade-off: photonic-integrated-circuits with diffractive optics offer scalability but have poor mode quality1,2, whereas inertially limited micromechanical scanners provide high-quality beams but lack scalable integration3,4. Here we report a photonic ski-jump-a nanoscale waveguide monolithically integrated on a piezoelectric cantilever-to overcome these limitations. It passively curls ~90° out-of-plane within a less-than-0.1 mm2 footprint, emits a submicrometre, broadband diffraction-limited beam, and exhibits kilohertz-rate mechanical resonances with quality factors of over 10,000. Fabricated in a volume complementary metal-oxide-semiconductor (CMOS) foundry, our device enables scalable two-dimensional beam scanning. Driven on-resonance at CMOS-level voltages, it achieves a footprint-adjusted spot rate of 68.6 mega spots s-1 mm-², exceeding state-of-the-art micro-electro-mechanical systems mirrors by more than 50-fold, which is sufficient for one million pixels at 100 Hz from an approximately 1.5 mm diameter footprint. We demonstrate full-colour image and video projection, and single-photon initialization and readout from silicon vacancy centres in diamond. Finally, by demonstrating uniformity across a 64 ski-jump array, we establish a pathway to achieving greater than one gigaspot resolution at kilohertz rates within a sub-5-cm-diameter footprint, creating a seamless optical pipeline between integrated photonic processors and the free-space world.