Yield curve models within the popular Nelson-Siegel class are shown to arise from formal low-order Taylor approximations of the generic Gaussian affine term structure model. Extensive empirical testing on government and bank-risk yield curve datasets for the five largest industrial economies shows that the arbitrage-free three-factor (Level, Slope, Curvature) Nelson-Siegel model generally provides an acceptable representation of the data relative to the three-factor Gaussian affine term structure model. The combined theoretical foundation and empirical evidence means that Nelson-Siegel models may be applied and interpreted from the perspective of Gaussian affine term structure models that already have firm statistical and theoretical foundations in the literature.