People who have not been exposed to math heavy content on a routine basis often have the unrealistic expectation of understanding everything on first read. That almost never happens unless the paper is very close to the reader’s own field of expertise. Denser papers, in fact, may take days of effort to fully internalize even for someone mathematically inclined and accustomed to reading papers.
For example, I also didn't remember why you needed a determinant in the equation you linked so I made a simple example and saw the determinant was there to keep the density normalized, (i.e the indefinite integral of the density = 1).
In this case, the simple example I used was a distribution q0(x) = 1 where x>=0 and x <= 1 (zero elsewhere) and scaling transformation y = ax