There are four bands that have used the name Ad Infinitum :

1. Ad Infinitum is a symphonic/power metal band with Melissa Bonny on vocals, Korbinian Benedict on bass, Niklas Müller on drums, and Adrian Thessenvitz on guitar.

2. Ad Infinitum is a space black metal project from Appalachia, Kentucky, founded in 2013 year by J.G.S. Its debut album called Woven Within was released in February 2014.

3. Ad Infinitum were a project headed by keyboardist Todd Braverman, formerly a member of the progressive rock band Cathedral. Their eponymous debut album from 1998 recreates 70s-style progressive rock inspired by bands like Genesis or Yes.
Musicians:
Mike "Goose" Seguso / vocals
Todd Braverman / keyboards, guitars
Craig Wall / guitars
Ilan Goldman / keyboards, vocals
Dave Beers / Bass
Don DiPaolo / Drums

Additionally, there was a collaboration between Peter Hook of New Order and the band Stockholm Monsters entitled Ad Infinitum. They recorded a one off 7 inch entitled Telstar that was backed with Telstar in a Piano Bar. This 7 inch was released in March of 1984.

4. Ad Infinitum were a black metal band from Austria that released one demo in 2002.