Looks like a dead end. Why CUDA? There should be some way to use Rust for GPU programming in general fashion, without being tied to Nvidia.
CUDA is the easiest-to-use and most popular GPGPU framework. I agree that it's unfortunate there aren't good alternatives! As kouteiheika pointed out, you can use Vulkan (Or OpenCL), but they are not as pleasant.
It defeats the purpose. Easy to use should be something in Rust, not CUDA.