[jofer]

Exactly!

Also, this broad approach of learning noise vs signal during interpolation is well known in the geostats world. There, you typically accomplish it by allowing a non zero "nugget" when you fit the variogram. However, folks in that community often prefer removing noise in post-processing despite having a robust statistical method to interpolate only the signal and not the noise. The reason is that the noise vs signal decision is highly application dependent, and it's easier to post-process differently than it is to run full solutions differently.

In other words, gaussian processes are also often used to interpolate signal and noise separately. Folks on that side are often very hesitant to do so, despite having well-established methods for it.

It's easy to remove things that are real and also easy to overfit noise. The same dataset needs different signal vs noise classifications depending on the end use case.

Put in other terms: One person's noise is another person's signal.