Infinite Drift tells the story of Astrid, a young woman, troubled by an ennui towards life. She spends her days sleepless and her nights alone, watching video's on the internet of trains in Norway. She is harassed daily by an American who calls her and claims she still owes him a large amount of money. Her only escape is her hypnotizing electronic music. One night she meets another likely and meandering soul, Ajab. Soon they form a strong and special connection. In a world where almost all meaning seems to be superficial, Ajab's arrival finally makes Astrid feel a sense of purpose.

After an unexpected encounter, Fleur and Julian fall madly in love. Soon after Julian proposes, an ambitious, yet challenging idea starts to dawn on Fleur. Slowly but surely, she works out a plan to get married in every country where she and her wife are allowed to do so. Fueled by their love and a rising sense of urgency, they take a leap of faith. After only four marriages, their journey comes to an inevitable, painful halt.