Random tiling models can exhibit three types of regions: frozen regions where all tiles are identical, rough regions where correlations decay polynomially, and smooth regions where correlations decay exponentially. Fluctuations at boundaries between these regions are expected to converge to the Airy line ensemble. This is understood in great generality at frozen-rough boundaries but much harder to establish at rough-smooth boundaries, where the smooth region contributes an underlying noise and the natural families of lattice paths associated to the boundary are undirected. In this talk, I will discuss one random tiling model, the two-periodic Aztec diamond, where we can overcome these difficulties and establish Airy line ensemble convergence at a rough-smooth boundary. Based on joint work with Sunil Chhita and Tom Finn.