I don’t think that neural networks are a natural approach for sampling
from high-dimensional distributions – not that I know what your
specific use case is.

Your distribution is described by a probability-destiny function that is
a function of the 10-100K coordinates of your high-dimensional space.
Can you compute reasonably efficiently the changes in the PDF as
you take “simple” steps that move you about in that space?

If so, the “standard” approach for sampling from such a distribution
is a Markov-chain Monte Carlo.

Thank you for your response. I was also recently looking into MCMC sampling methods and will look deeper after your advise. Normalizing Flows seems to be the most popular approach but I am unsure if they’re scalable enough for my use-case or would need too much additional parameters to be trained.