A leak detection tool is positioned in in a tubing string that is disposed in a wellbore. The leak detection tool is attached to a downhole end of a line and includes a cup. An outside diameter of the cup is substantially the same as an inside diameter of the tubing string. An uphole end of the line is attached to a spool disposed proximate to an uphole end of the wellbore. The leak detection tool is propelled through the tubing string in a downhole direction by pumping a fluid down the tubing string such that a fluid pressure uphole of the cup is greater than a fluid pressure downhole of the cup. A flow of fluid from an interior of the tubing string uphole of the cup to an exterior of the tubing string through a leak in a wall of the tubing string is detected as the cup passes the leak. A depth of the leak is determined based on a length of the line from the spool to the leak detection tool when the flow of fluid from uphole of the cup through the leak is first detected.