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The conventional Galton board illustrates diffusion in a classical-mechanics context: it is composed of balls performing a random walk on a downward sloping plane with a grid of pins. We introduce a wave-mechanical variety of the Galton board to study the influence of interference on the diffusion. This variety consists of a wave, in our experiments a light wave, propagating through a grid of Landau-Zener crossings. At each crossing neighboring frequency levels are coupled, which leads to spectral diffusion of the initial level populations. The most remarkable feature of the spectral diffusion is that below a certain single-crossing transition probability (around 0.7--0.8) the initial spectral distribution almost perfectly reappears periodically when the wave penetrates further and further into the grid of crossings. We compare our experimental results with numerical simulations and with an analytical description of the system based on a paper by Harmin [Phys. Rev. A 56, 232 (1997)].