We report on a peculiar propagation of bosons loaded by a short Laguerre–Gaussian pulse in a nearly flat band of a lattice potential. Taking a system of exciton polaritons in a kagome lattice as an example, we show that an initially localized condensate propagates in a specific direction in space, if anisotropy is taken into account. This propagation consists of quantum jumps, collapses, and revivals of the whole compact states, and it persists given any direction of anisotropy. This property reveals its signatures in the tight-binding model, and, surprisingly, it is much more pronounced in a continuous model. Quantum revivals are robust to the repulsive interaction and finite lifetime of the particles. Since no magnetic field or spin–orbit interaction is required, this system provides a new kind of easily implementable optical logic.