A new and unique plant cultivar of perennial carnation or pinks, Dianthus plant named ‘;Appleblossom Burst’; with numerous, medium-sized, semi-double, lightly-fragrant flowers producing a rounded slightly mounded face. The numerous, well-branched stems cover top to bottom of clump with multiple flowers per stem. Petals open light pink blushed with medium pink and lighten in maturity to white to white with faint pink blush. Center of flowers has a dark red eye, and petal tips have fine serrations. The habit is compact with narrow, bluish-green foliage.