The sisters, who have historically had a difficult relationship, told People that they agreed to the diving competition in an attempt to build bridges.
Kim said that she "really didn't see any light at the end of the tunnel", describing her troubles with her sister as a "rough patch over the last couple of years".
"I thought [The High Dive] would be a nice opportunity for Kyle and I to really bond," she said. "It took us actually a step beyond closer. We're probably the closest we've maybe ever been."
Meanwhile, Kyle explained that she was "overcome by fear" when facing her first dive but explained that Kim helped her to get through her anxiety.
"My sister felt very protective of me and kind of went into mama-bear mode," she said. "We really had to support each other and I think that's the best thing that's come out of this for us. Kim and I are definitely in the best place we've been since we were little girls."
The Real Housewives of Beverly Hills airs Mondays on Bravo in the US.