Born in Chemnitz, Wulf grew up in Krakow, where he received a rabbinical education. Between 1941 and 1943, Wulf was active in the resistance in the ghettos of Krakow and Bochnia. In 1943, the Germans deported him to Auschwitz. During one of the death marches of 1945, he was able to flee. His wife and son survived, hidden by a Polish farmer.
After the war, he worked for the Central Jewish Historical Committee in Poland for two years. In 1947, while living in Paris, Wulf co-founded the Centre pour l’Histoire des Juifs Polonais (Centre for the History of Polish Jews). During his stay, he met Léon Poliakov. They would go on to publish several books together.