An invertible transformation from a base density to a sample space supports forward sampling and allows a sample's probability to be calculated by mapping it back to the base density.

“If you make sure that this density is invertible,”

“Technically a little bit less is possible, but say it's invertible.”

“Then uh we can actually uh both do the sampling, so you go from the base sensitivity, you go forward to the sample space uh so this is the sampling direction. And if you have a sample, you can go backward and figure out the the probability of generating something by looking at uh what it is on the normal. So this is the first idea which you can kind of branch off from. And the second is from optimal transport.”