The singer used a sample of 1-year-old Bingham's heartbeat for The 2nd Law album track 'Follow Me', and explained that fatherhood has changed his approach to music.
"Becoming a father has made my songwriting a bit more focused. I don't think it's affected my concerns and fears and anxieties. If anything, the concerns for the future are amplified," Bellamy told NME.
The frontman also admitted that another track on the album centres around an argument he had with fiancée and Hollywood actress Kate Hudson.
"It's like you've had a fight with your girlfriend and she goes off to her mum's house for the day and you're on your own going, 'What did I say?'," he explained of the track.
"I'm sure a lot of blokes have that experience in the early stages of relationships where you go, 'Yeah, she's right isn't she?'"
Muse will release their new album The 2nd Law in the UK on September 17 and a day later in the US.
Watch the music video for Muse's new single 'Survival' below: