I could write a poem like this: I take the titles of Ashbery's 20 part series based on Czerny exercises. I read a poem by Ashbery, with a certain title, and take that title as my own, writing my own poem. It can't be a variation of the Ashbery poem, or take anything from it, but must be my own response to his title, which he in turn borrowed from a book of piano exercises.
Then--and this is the crucial step--I give a new title to it, using something suggested to me by my poem, so no trace of Ashbery is left any more. So why do I need Ashbery in the first place? I don't, but I wouldn't have started without this particular poem of his. I'm neither imitating his style nor trying to avoid it; it's merely Ashbery-adjacent.
Sometimes the best ideas happen like that. There is no remaining connection to the original inspiration, but the idea would not have occurred without that stimulus.