Preheat your oven to 350°F (175°C) and prepare a muffin tin with liners.
In a large bowl, combine the applesauce, sugar, vegetable oil, and vanilla extract. Stir until well mixed.
In another bowl, whisk together the flour, baking soda, cinnamon, and salt.
Gradually add the dry ingredients to the wet mixture, stirring gently until just combined.
Fold in chopped nuts or raisins if desired.
Spoon the batter into the prepared muffin tin, filling each cup about two-thirds full.
Bake for 20-25 minutes, or until a toothpick inserted in the center comes out clean.
Remove from the oven and let cool in the pan for 5 minutes.
Transfer muffins to a wire rack to cool completely.