I present results on the quantum dynamics of a minimal model with spatial structure and local interactions. The model features a time-independent Hamiltonian, in contrast to the widely studied quantum circuits, and is analytically tractable in the limit of large local Hilbert space dimension and weak intersite coupling. In this regime, I show that the energy dynamics are governed by a classical master equation exhibiting diffusive behavior. Furthermore, I demonstrate that the spectral form factor can be expressed exactly in terms of the solution to this master equation, demonstrating how the linear ramp emerges at long times, while locality gives rise to an additional enhancement at short times.