In a small bowl, combine the cream cheese, sugar and milk until smooth. Fold in 1-1/2 cups whipped topping. Spoon into crust.
In a large bowl, whisk cold milk and pudding mixes until combined. Stir in the pumpkin, cinnamon, ginger and cloves.
Spread over cream cheese layer. Spread with remaining whipped topping. Refrigerate for at least 3 hours before cutting.