Despite its only release on the soundtrack for Lara Croft: Tomb Raider, the "Deep" video clip is completely unrelated to the movie. The video features Reznor as a bank robber who, together with a girl, steals two boxes from the national mint. They believe these boxes contain cash but instead contain a highly toxic dye, which sprays all over them when they (separately) attempt to open the boxes. Rushing to warn each other, their cars collide head on. The narrative occurs in reverse order during the clip, with the car accident at the beginning and the decision by the thieves to retrieve the boxes (to "make a withdrawal") at the end.
Reznor has made it clear on numerous interviews that he was disappointed by how the video turned out.