The 40-year-oldactor first stepped out with Chung, 33, in June 2015 but the two never spoke about their relationship.
"No one cheated on anyone. It was a clean breakup that was caused by busy schedules and distance. They really did love each other and were pretty serious. They still have respect for each other," a source confirmed E! Online.
However, according to various publications Skarsgard was recently set up on a blind date with Toni Garrn.
Skarsgard and Garrn reportedly went out together in Montauk, New York, this past weekend.