Generative modeling of conditional probability distributions on the level-sets of collective variables

arXiv:2512.17374v3 Announce Type: replace Abstract: Given a probability distribution $\mu$ in $\mathbb{R}^d$ represented by data, we study in this paper the generative modeling of the corresponding conditional probability distributions on the level-sets of a collective variable $\xi:\mathbb{R}^d \rightarrow \mathbb{R}^k$, where $1 \le k