I think there is still some concepts are getting confused here:
- The default transform does the right thing, because it is mapping values in the unconstrained space to the right domain
- The default random also does the right thing, as it is producing random sample regardless of what transformation in the inference time it is doing, as long as it is volume preserved.
Problem you are describing are: user specified transformation that change the domain of the distribution, for example, a sum to 1 transformation on Uniform distribution. In this case, the random method would be wrong as the transformation is modifying the domain instead of just unbounding the free parameter.
In a way, we are speaking about 2 operation here, and the current transform kwarg only deal with [1] (unbounding a constrained parameter), but not intended to solve [2] (transforming a distribution into another) although we could use it to partially solve [2].