Author of VAE/diffusion model papers here.

When a paper introduces something as intractable, it typically means that it can't be computed exactly in a computationally feasible way, which forms a motivation for using approximations. The challenge is then to come up with an approximation that has nice properties (e.g computationally cheap, unbiased, is a bound, etc.).

As another commenter also wrote, how an idea is presented in the paper is typically different from how the author(s) came up with the idea. At the start of a research project you often start with a concrete problem and some vague intuitions on how to solve it. Then through an iterative process you refine your ideas. Often it turns out that what you wanted to do is impossible. Often it turns out that a solution already exists so there's no need to publish. The process often requires lots of backtracking, scrapping dead ends, and it often requires time before an idea finally 'clicks' in your mind (which is a great feeling). Especially when you start out in research, nine out of ten ideas turn out to be either already solved, or (seemingly) unsolvable, which can be very frustrating. And Since negative results are typically unpublishable or uninteresting, you don't read about them. The flip side is that with more experience, you build a bigger mental toolbox, making it easier spot dead ends and see opportunities. The best way to get is there is to read ML books (or other media) that teach you the underlying math, and lots of practice.