The song reunites Cornell with his Soundgarden bandmates for the group's first single in more than 15 years.
In an interview with The Hollywood Reporter, the singer discussed the pressure of recording a comeback single that is also featured in one of the year's most highly anticipated films.
"This song came arduously. It's different, because it has to be a Soundgarden song," Cornell explained. "It has to resonate with every band member. Writing a song for the Avengers film, it has to be lyrically not specific to the movie or the story, but it has to work with it. It wasn't so easy. But it turned out absolutely a Soundgarden song."
Cornell also marveled at how much the music industry has changed since Soundgarden released their last album Down on the Upside in 1996.
"It's such a different environment. In this day and age, you don't have the monolithic record company with seemingly limitless resources and multimillion-dollar profits. They don't exist," the musician said.
"The movie company does have [resources], and they will promote ['LIve to Rise']. It's the only way to get your music in front of people - that and the age-old way of getting out there and playing. There was a time when the idea of staying at home sounded good. That's long since gone," he continued.
"It's a privilege to be able to travel the world and play music you wrote for people. Millions of people write songs no-one will hear except a few who follow them on Facebook and their grandparents, who begrudgingly listen because they love their grandchildren."
The Avengers stormed the US box office over the weekend, taking more than $200m in three days.
Watch Soundgarden's 'Live To Rise' music video below: