What is the opposite to "discretization"? Solving an initially continuous problem using discrete math tools is known as "discretization".
Does the opposite option of using continuous tools to solve discrete problems have a name? And if not, is there any reason why?

Coming from natural language processing, that would apply for instance to resorting to word-embeddings, where one expresses words as vectors in order to escape from the essentially discrete nature of word combinatorics. In econometrics, that could apply to the standard modelling of discrete choices, where a fictional continuous quantity (utility) is maximised... and the list probably goes on for ever.

It seems to be an embedding as you already wrote. Check this Wikipedia entry: https://en.m.wikipedia.org/wiki/Embedding
The function or process could be called embedding or maybe continuity approximation.
