Optomechanical devices sensitively transduce and actuate motion of nanomechanical structures using light. Single--crystal diamond promises to improve the performance of optomechanical devices, while also providing opportunities to interface nanomechanics with diamond color center spins and related quantum technologies. Here we demonstrate dissipative waveguide--optomechanical coupling exceeding 35 GHz/nm to diamond nanobeams supporting both optical waveguide modes and mechanical resonances, and use this optomechanical coupling to measure nanobeam displacement with a sensitivity of $9.5$ fm/$sqrt{text{Hz}}$ and optical bandwidth $>150$nm. The nanobeams are fabricated from bulk optical grade single--crystal diamond using a scalable undercut etching process, and support mechanical resonances with quality factor $2.5 times 10^5$ at room temperature, and $7.2 times 10^5$ in cryogenic conditions (5K). Mechanical self--oscillations, resulting from interplay between photothermal and optomechanical effects, are observed with amplitude exceeding 200 nm for sub-$mu$W absorbed optical power, demonstrating the potential for optomechanical excitation and manipulation of diamond nanomechanical structures.
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