  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.
