Bead-spring systems in spatially periodic potentials, such as the Frenkel–Kontorova model, exhibit complex behavior due to the interplay of elastic spring energies and external potentials. Here, we study the one-dimensional diffusion of a trimer, three beads connected by springs. In our system, all beads feel a sinusoidal external potential, but with different amplitudes. Using Langevin dynamics simulations and analytical expressions in limiting cases, we show that the diffusion constant of this system exhibits non-monotonic behavior, depending on the spring stiffness. The elastic coupling of the springs can slow down diffusion by anchoring faster beads to slower ones or accelerate it by annihilating potential barriers of different signs.