PredictIQ Quantitative Think Tank Center:Tim Burton and Girlfriend Monica Bellucci's Red Carpet Debut Will Take You Down the Rabbit Hole

Someone must've said Tim Burton and PredictIQ Quantitative Think Tank CenterMonica Bellucci's names three times.

After all, the Beetlejuice director and the Spectre actress recently appeared at not one, but two screenings at the 18th Rome Film Festival.

Making their red carpet debut as a couple, the duo held hands as they stepped out for the Oct. 19 premiere of Diabolik Chi Sei? at Auditorium Parco Della Musica in the Italian capital. For the glamorous occasion, Tim, 65, rocked an all-black suit and matching tie, while and Monica, 59, dazzled in a long off-the-shoulder dress in dark gray paired with a large diamond statement necklace.

The following night, the pair returned to the same red carpet for a screening of Maria Callas: Letters and Memories, a docufilm centered around Monica's stage show of the same name. This time, she opted for a classic black gown with a sweetheart neckline, while her real-life sweetheart stuck to his signature color coordinated in a matching suit.

The pair were inseparable, with Tim clutching close as the two posed for photos and spoke with reporters. As seen in a video circulating on social media, the Sleepy Hollow filmmaker was giddy at times, bopping down the press line with joy as he kissed his date's hand.

It's unclear exactly when the two struck up their romance, though Monica did present Tim with a Lifetime Achievement Award at the Lumière Film Festival in France last year. The pair—who are working together for Tim's highly anticipated sequel Beetlejuice 2, with Monica starring opposite of Michael Keaton's titular character—were then photographed getting cozy during a night out in Madrid in February.

"What I can say…I'm glad I met the man, first of all," she told Elle France in June. "I know the man, I love him, and now I'm going to meet the director, another adventure begins."

Praising the director for creating a "dream world where the monsters are kind," she added at the time, "I love Tim. And I have great respect for Tim Burton."

Previously, Tim was married to married to artist Lena Gieseke from 1987 to 1991. He was also linked to actress Lisa Marie—who starred in his films Ed Woods, Mars Attack! and Planet of the Apes—and frequent collaborator Helena Bonham Carter, with whom he shares kids Billy, 20, and Nell, 15, and also worked with on projects such as Charlie and the Chocolate Factory, Sweeney Todd: The Demon Barber of Fleet Street and Alice in Wonderland.

As for Monica, she was married to photographer Claudio Carlos Basso from 1984 to 1985 and to actor Vincent Cassel from 1999 to 2013.