Place cranberries into a saucepan and pour in pomegranate juice. Cover and bring to a boil until cranberries begin to pop. Reduce heat to medium and stir sugar into cranberry mixture. Cook, mashing often with a spoon or potato masher, until cranberries have broken, about 5 minutes. Cover and reduce heat to low; simmer to fully dissolve sugar, 2 to 3 minutes. Stir walnuts into cranberry sauce before serving. Transfer into a serving dish and chill before serving.
