  Nitrogen-vacancy (NV) centers in diamond have emerged as valuable tools for
sensing and polarizing spins. Motivated by potential applications in chemistry,
biology, and medicine, we show that NV-based sensors are capable of detecting
single spin targets even if they undergo diffusive motion in an ambient thermal
environment. Focusing on experimentally relevant diffusion regimes, we derive
an effective model for the NV-target interaction, where parameters entering the
model are obtained from numerical simulations of the target motion. The
practicality of our approach is demonstrated by analyzing two realistic
experimental scenarios: (i) time-resolved sensing of a fluorine nuclear spin
bound to an N-heterocyclic carbene-ruthenium (NHC-Ru) catalyst that is
immobilized on the diamond surface and (ii) detection of an electron spin label
by an NV center in a nanodiamond, both attached to a vibrating chemokine
receptor in thermal motion. We find in particular that the detachment of a
fluorine target from the NHC-Ru carrier molecule can be monitored with a time
resolution of a few seconds.
