Hydrodynamic coordination of cilia is ubiquitous in biology. It is commonly modeled using the steady Stokes equations. The flow around ciliated cells, however, exhibits finite-time vorticity diffusion, requiring a dynamical description. We present a model of elastic cilia coupled by unsteady viscous flow in the bulk fluid. Therein, vorticity diffusion impacts cilia coordination qualitatively and quantitatively. In particular, pairs of cilia synchronize in antiphase for long diffusion times. Moreover, metachronal waves occur in cilia chains larger than the viscous penetration depth, whereas global synchronization occurs in Stokes flow.