The 50-year-old rocker felt the presence of his late friend - who died of cancer in January 2016 - while he was in the recording studio working on 'Zowie', a tribute track to the 'Jean Genie' hitmaker which appears on his new record 'Ogilala'.
He said: ''When I was writing the song, the opening chord sequence reminded me of, like, the kind of chords David [would use] ... he'd do a lot of weird inversions.
''He was just in the air and so he kind of rode shotgun with me when I was writing this song.''
And that isn't the only supernatural experience the Smashing Pumpkins singer - who is now recording under his full name, William Patrick Corgan - experienced recently.
The 'Tonight, Tonight' hitmaker recalled how he was writing in one room in his house, while his girlfriend, Chloe Mendel, was cooking in the kitchen.
He said: ''I hit some weird key and the thing blanked and I lost eight day's worth of work.''
At the exact same time, Chloe saw a vision of a woman in the kitchen which looked like Billy's mother when she was 25, and the two ran to find one another to share what had happened to them.
Billy - who was unable to retrieve his work - said: ''It was like this weird ripple in time thing.''
And the 'Bullet With Butterfly Wings' singer also claimed he once encountered a shapeshifter, though he refused to be drawn on the details.
Speaking to Sirius XM DJ Howard Stern, he said: ''Let's just say I was with somebody once and I saw a transformation that I can't explain... I saw it. I was totally sober...
''Imagine you're doing something, you turn around and suddenly there's somebody else standing there. [A different human?] Sort of. It's hard to explain without going to detail, I'd rather not going into detail.
''They acknowledged it [but] they wouldn't explain.
It's a really messed up story. No [not a famous person]. I'm being vague on purpose.
''It's up there with one of the most intense things I've ever been through.''