We compare two methods for analyzing periodic dimer models. These are the matrix-valued orthogonal polynomials approach due to Duits and one of the authors, and the Wiener–Hopf approach due to Berggren and Duits. We establish their equivalence in the special case of the Aztec diamond. Additionally, we provide explicit formulas for the matrix-valued orthogonal polynomials/Wiener–Hopf factors in the case of the 2×2-periodic Aztec diamond in terms of Jacobi theta functions related to the spectral curve of the model.