Line muffin tins with liners or spray with cooking spray.
In a large bowl, combine flour, bran, baking powder and baking soda until well mixed.
In a medium size bowl, whisk the egg whites, and molasses until frothy.
Whisk in the applesauce and milk.
Pour the liquid mixture in with the dry ingredients and stir until just combined, but do not over stir. (if desired, this can be left in the refrigerator over night, covered.) The fruit should not be added until just before baking.
Very gently fold in the raspberries, (try to prevent the fruit from breaking.) Spoon an heaping 1/4 cup of the batter into each muffin cup, filling each completely.
Bake for 25 minutes until golden brown.
Remove the muffins from the tins and transfer to a wire rack to cool.