Diamond offers unique material advantages for the realization of micro- and nanomechanical resonators because of its high Young's modulus, compatibility with harsh environments and superior thermal properties. At the same time, the wide electronic bandgap of 5.45 eV makes diamond a suitable material for integrated optics because of broadband transparency and the absence of free-carrier absorption commonly encountered in silicon photonics. Here we take advantage of both to engineer full-scale optomechanical circuits in diamond thin films. We show that polycrystalline diamond films fabricated by chemical vapour deposition provide a convenient wafer-scale substrate for the realization of high-quality nanophotonic devices. Using free-standing nanomechanical resonators embedded in on-chip Mach-Zehnder interferometers, we demonstrate efficient optomechanical transduction via gradient optical forces. Fabricated diamond resonators reproducibly show high mechanical quality factors up to 11,200. Our low cost, wideband, carrier-free photonic circuits hold promise for all-optical sensing and optomechanical signal processing at ultra-high frequencies.