  We report on the design, fabrication and measurement of travelling-wave
superconducting nanowire single-photon detectors (SNSPDs) integrated with
polycrystalline diamond photonic circuits. We analyze their performance both in
the near-infrared wavelength regime around 1600 nm and at 765 nm. Near-IR
detection is important for compatibility with the telecommunication
infrastructure, while operation in the visible wavelength range is relevant for
compatibility with the emission line of silicon vacancy centers in diamond
which can be used as efficient single-photon sources. Our detectors feature
high critical currents (up to 31 {\mu}A) and high performance in terms of
efficiency (up to 74% at 765 nm), noise-equivalent power (down to 4.4*10^-19
W/(Hz^1/2) at 765 nm) and timing jitter (down to 23 ps).
