Kunigunde was the only daughter of Welf II, Count of Altdorf, and Imiza of Luxembourg. She was named after her mother’s aunt Cunigunde, who was married to Emperor Henry II. Her brother was Welf III (died 1055), the last member of the Elder House of Welf.
Kunigunde married c. 1035 to Albert Azzo II, Margrave of Milan, Luni, and Tortona. He was the only son of Albert Azzo I and his wife Adelaide. Kunigunde's dowry included the estate of Elisina (modern Solesino) which had formed part of her mother, Imiza’s dowry.
Kunigunde and Albert Azzo had one son: