Preheat the oven to 350°F. Lightly spray a 9x5-inch loaf pan with nonstick spray.
In a large bowl, mix together the sugar, eggs, oil and vanilla. In a separate bowl, whisk together the flours, baking powder and soda, and spices, and add them to the wet ingredients in the bowl. Mix in the oats, applesauce and walnuts (if using).
Pour the batter into the prepared pan, and bake 40 to 50 minutes, until a toothpick comes out clean when you poke it into the middle of the bread. Remove the bread from the oven, and cool completely.