To just link this with no context, it really needs an intro that summarizes in one sentence what it actually does. The description currently reads like a bunch of technobabble.

I agree. One image of what it is doing would improve the comprehension of the algorithm.

For folks asking what it does in general, see https://en.wikipedia.org/wiki/Image_registration

This method is meant for working with multiple images where something has significantly changed in a non-linear way. E.g. think of trying to produce a deformation map of clay that you've squeezed by taking lots of photographs during squeezing. You can also use it in the reverse sense and align multiple images where things are changing in complex ways. The fact that inverts for / is constrained by a continuous velocity field has some nice advantages compared to other methods. Or that's my bad summary of it, anyway.

As someone who uses this general class of methods pretty frequently (albeit in satellite imagery), I'm very curious to dig into this! Looks like a very understandable set of implementations!