Boil the potatoes: Add diced potatoes to a pot of salted water. Bring to a boil and cook until tender, about 10–15 minutes. Drain and let cool slightly.
Prepare the deviled egg mixture: Mash the yolks of the hard-boiled eggs with mayonnaise and Dijon mustard. Mix until smooth, then fold in the chopped egg whites and diced celery.
Combine potatoes and egg mixture: Gently fold the cooled potatoes into the egg mixture. Mix carefully to avoid mashing the potatoes.
Season and garnish: Add salt and pepper to taste. Sprinkle with paprika and chopped chives if desired.
Chill and serve: Refrigerate for at least 30 minutes before serving. Serve cold for best flavor.