For inverse transform sampling, if you know the CDF of a probability distribution ($f_X$) that you want to sample, you can generate a uniform realization ($U$) from [0,1], and then according to the sampling theorem,
My question is that can you replace the $U$ (the sample comes from uniform distribution [0,1]) with a sample coming from a Gaussian distribution?
I asked this question because according to here, it says:
Any distribution in d dimensions can be generated by taking a set of d varaible that are normally distriuted and mapping them through a sufficiently complicated function (e.g, In one dimension, you can use the inverse cumulative distribution function (CDF) of the desired distribution composed with the CDF of a Gaussian. this is an extension of "inverse transform sampling". )