1. In a small bowl, combine the applesauce and oats. Set aside for 5 minutes.
2. In a large bowl, combine the flour, sugar, baking soda, baking powder, and cinnamon, and stir to mix well. Add the applesauce mixture and the egg whites to the flour mixture, and stir just until the dry ingredients are moistened. Fold in the cranberries.
3. Coat an 8-x-4-inch loaf pan with nonstick cooking spray. Spread the batter evenly in the pan, and bake at 350°F for about 45 minutes, or just until a wooden toothpick inserted in the center of the loaf comes out clean.
4. Remove the bread from the oven, and let sit for 10 minutes. Invert the loaf onto a wire rack, turn right side up, and cool to room temperature before slicing.