Tor Erik Hermansen:

We had been working with [“Diamonds” co-producer] Benny Blanco on a number of Rihanna songs, trying to come up with these big, uptempo, dance-pop records [for 2012’s Unapologetic]. During the last couple of days, we were like, “Let’s just do something completely different — different tempo, different everything.” That’s how the track started. Sia came through and worked on a couple different songs, and the last thing she did before walking out the door was “Diamonds.” The car was waiting outside. She had her coat on, she had her purse in her lap. We just played her the music, and the first thing out of her mouth was, “Shine bright like a diamond.” She put her vocal down in about 12 minutes while the car was waiting and then left. Rihanna heard it and loved it straight away. Rihanna really went to work on that song because she wanted to capture that character that Sia has in her voice. I think she spent two or three days recording that song, which is very rare. Normally you do it in a day or half a day. It was very important for her to capture that feeling, and she did it so well that Sia thought it was her [own voice on the song]. I think Mikkel opened up the song [file] to prove to Sia that it was Rihanna singing.

Via EW

Also, according to Songfacts Rihanna told iHeartRadio:

You’re not sad. You’re happy and hippie. It’s hopeful. It gives me a great feeling when I listen to it. The lyrics are hopeful and positive. It’s about love and the gears are different than what people will expect.

Rihanna said in an interview with MTV that “I think a lot of people are afraid of being happy because of what others might think of it. They’re afraid to embrace that and embrace themselves and love themselves and do what they love and do what makes them happy. My story is definitely going to be a happily ever after, no matter what.”

Meaning that Rihanna will ‘Shine bright like a diamond’ and will always do what makes her happy.

“Diamonds” was prominently used in the 2014 French coming-of-age movie Girlhood. Director Celine Sciamma actually wrote and filmed the scene in which the song was used before securing the rights. In post-production, she sent the hotel scene to Rihanna and her team, and they loved the clip so much, they signed off on the rights for Sciamma to keep the song in the film. Sciamma said that:

The song is really anthem of sisterhood. I loved the song when it first came out and just imagined the lyrics coming out of the mouths of these characters."