Step 1: Identify what crystallizes.
Diopside has the ideal composition \(\mathrm{CaMgSi_2O_6}\). Its crystallization removes \(\mathrm{CaO}\) and \(\mathrm{MgO}\) from the melt in roughly comparable proportions, while it does not incorporate \(\mathrm{Al_2O_3}\).
Step 2: Predict melt evolution.
Because crystals take up Ca and Mg, the residual melt becomes depleted in both \(\mathrm{CaO}\) and \(\mathrm{MgO}\). Hence, starting from \(X\), the melt composition should move toward lower CaO (downward on the CaO axis) and lower MgO (leftward on the MgO axis).
Step 3: Match with the arrows.
Among the indicated trends, only arrow III points down-left, i.e., to lower CaO and lower MgO, which correctly represents the residual melt evolution during diopside crystallization.
\[
\boxed{\text{Arrow III (Option C)}}
\]