  Spatial non-uniformity in tight-binding models serves as a source of rich
phenomena. In this paper, we study a diamond-chain tight-binding model with a
spatially-modulated magnetic flux at each plaquette. In the numerical studies
with various combinations of the minimum and maximum flux values, we find the
characteristic dynamics of a particle, namely, a particle slows down when
approaching the plaquette with $\pi$-flux. This originates from the fact that
the sharply localized eigenstates exist around the $\pi$-flux plaquette. These
localized modes can be understood from a squared model of the original one.
This characteristic blocked dynamics will be observed in photonic waveguides or
cold atoms.
