Preheat oven to 350°F (175°C). Grease a 12-cup muffin tin or line with paper liners.
In a large bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, mix together pumpkin puree, vegetable oil, eggs, and sugar until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in the chopped walnuts.
Divide the batter evenly among the muffin cups.
Bake for 20-25 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.