Noren shot his second straight 66 in the second round. Molinari added a 70 to his course-record-setting first-round 62.
"My last nine holes I played really well the whole nine, and it felt a lot better coming in with the 66 today than the 66 yesterday," Noren said.
S.S.P. Chowrasia (67) was in fifth and a group of players, including world No. 1 and defending champion Luke Donald (68), were another stroke back.
The tournament is being played at the Castle Stuart Golf Links in Inverness.