The dynamics of athermal polymer blends with stiffness disparities are studied using computer simulations of the bond-fluctuation model. For mixtures of ten-mer chains, we see a difference in the temperature dependence of the diffusion coefficients of the two blend components for all blend compositions with appreciable amounts of the more flexible component. Hence, our model system can qualitatively capture the composition dependence of dynamic heterogeneity that is observed experimentally in miscible polymer blends. While blends of ten-mer chains display clear evidence for dynamic heterogeneity, the dynamics of the two components in blends of dimers are identical over the entire temperature range studied. Shorter chain systems experience smaller concentration fluctuations and smaller contributions from chain connectivity, suggesting that local concentration variations play a critical role in the dynamic heterogeneity that is observed experimentally in miscible polymer blends with weak interactions. The diffusion coefficient of dilute flexible chains in a matrix of stiff chains is identical to the diffusion coefficient of the matrix chains at all temperatures, clearly demonstrating that inherent mobility differences of the two chains cannot solely explain blend dynamics.