In 2016 Blume won the 50 metre freestyle event at the Danish open gala. She was subsequently selected to compete at the 2016 Summer Olympics in Rio de Janeiro, Brazil, where she won 50 metre freestyle and also competed in 100 metre freestyle, the 4 × 100 metre freestyle relay and the 4 × 100 metre medley relay where she anchored the medley and thereby contributed to the Danish team winning a bronze medal, just 0.01 seconds behind the Australian team who won the silver medal.