CUDA largely was Nvidias attempt at swaying Khronos and Microsoft's DirectX team. In the end, Khronos went with something based on a blend of AMD's and Nvidia's ideas, and that became Vulkan, and Microsoft just duplicated the effort in a Direct3D-flavored way.
So, just use Vulkan and stop fucking around with the Nvidia moat.
A great thing about CUDA is that it doesn't have to deal with any of the graphics and rendering stuff or shader languages. Vulkan compute is way less dev friendly than CUDA. Not to mention the real benefit of CUDA which is that it's also a massive ecosystem of libraries and tools.
As much as I wish it were otherwise, Vulkan is nowhere near a good alternative for CUDA currently. Maybe eventually, but not without additions to nothing the core API and especially available libraries.