Replacing one ingredient with another in a recipe sometimes requires more than a straight substitution. While tomato puree and diced tomatoes contain the same basic ingredient, they add completely different flavors and consistencies to a dish. Tomato puree is usually cooked into the dish to provide thickness and flavor, while diced tomatoes work well as a garnish or finishing touch. Despite their differences, the two can be substituted for each other successfully in certain recipes.
First asses the dish carefully to determine if this a recipe where a substitution might work. If you are making a fairly wet, liquid dish -- such as a stew, chili or soup -- chances are you can swap diced tomatoes for tomato puree, though the texture and flavor of the final dish will be somewhat different. If your recipe relies on the texture of diced tomatoes, however -- such as in the case of salsa -- you should not make the substitution.
Measure out an amount of tomato puree equal to the amount of diced tomatoes required in the recipe.
Add the tomato puree to the recipe well before you would have added the diced tomatoes. The tomato puree can better handle long cooking times; diced tomatoes will become soggy and eventually disintegrate. Also, cooking the puree for longer will help incorporate its flavor into the rest of the recipe.