The 21-year-old singer has grown increasingly close to her 'Problem' collaborator and both she and the rapper - whose engagement to 'Glee' actress Naya Rivera ended in April - are ''doing great''.
A source told E! News: ''They have been friends since they made the song together. They have been spending more time together and recently have been getting very close. They are both doing great.''
The new couple were recently spotted at The Grove in Los Angeles following a late showing of 'The Purge'.
One onlooker claims they arrived partway through the movie and left before the end, but were still recognised by ''about three people''.
The source also insisted he spotted them kissing during the screening.
The news comes just a week after it emerged Ariana had split from boyfriend Jai Brooks, reportedly because he had been unsupportive following her grandfather's death.
A source said recently: ''When her grandfather was dying, everyone was there for her. People flew to Florida to be with her, but Jai didn't.
''Ariana just felt he wasn't there like he should have been.''
Despite a difficult July, the 'Bang Bang' singer recently admitted she is looking ahead to the future.
She tweeted: ''August is about to be a beautiful, beautiful month. Looking forward to all the good coming up.''
Corgan took to Instagram to confirm rumours of new Pumpkins material, saying the first songs could arrive as early as May.