AMD is working on a cudnn comptability layer iirc (MiOpen) and is ROCm group has created a cuda transpiler (to intermediary HIP then to amd binary via hcc)
https://instinct.radeon.com/en/6-deep-learning-projects-amd-...
https://instinct.radeon.com/en/6-deep-learning-projects-amd-...
Edit: OK I was reading the docs, I think I got it: hipDNN is a wrapper that (once finished) will search and replace calls (from cuDNN to hipDNN), then hipDNN itself, in turn, will call MIOpen, not sure if that's right, I would appreciate if someone who knows more could confirm
If they'd chosen one approach 5 years ago and put decent resources behind it they might be competitive by now.