Mesoscopic fluctuations reveal stochastic dynamics of molecules in both inanimate and living matter. Using motile cilia as a model, we connect noisy oscillations and small-number fluctuations of force-generating molecular motors. We develop a stochastic model of cilia beating and compare its predictions to experiments on reactivated Chlamydomonas axonemes, in which the number of molecular motors is systematically reduced. These experiments quantified cilia beat parameters as functions of motor number, including the quality factor, which measures oscillator precision. Using simulation-based inference, we compare this perturbation series to the stochastic model and infer microscopic motor parameters. We find that the stochastic model reproduces the experimentally observed quality factor and its reduction following motor extraction. The model also accounts for the emergence of phase defects in intra-cilium synchronization. Thus, fluctuations in the number of bound motors are sufficient to explain active beat fluctuations in cilia. Our approach establishes a link between microscopic motor noise and mesoscopic non-equilibrium dynamics, and illustrates a general strategy for testing theories of motor control using active fluctuations and controlled perturbation experiments as additional observables.