Preheat your oven to 350°F (175°C) and line a muffin tin with paper liners.
In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, salt, cinnamon, and nutmeg.
In another bowl, mix the applesauce, vegetable oil, and vanilla extract.
Pour the wet ingredients into the dry ingredients and stir until just combined. Fold in the diced apples.
Divide the batter evenly among the muffin cups.
Bake for 25 minutes or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.