Bridging discrete and continuous state spaces: Exploring the Ehrenfest process in time-continuous diffusion models

arXiv:2405.03549v1 Announce Type: cross
Abstract: Generative modeling via stochastic processes has led to remarkable empirical results as well as to recent advances in their theoretical understanding. In principle, both space and time of the processes can be discrete or continuous. In this work, we study time-continuous Markov jump processes on discrete state spaces and investigate their correspondence to state-continuous diffusion processes given by SDEs. In particular, we revisit the $\textit{Ehrenfest process}$, which converges to an Ornstein-Uhlenbeck process in the infinite …

abstract advances arxiv continuous cs.lg diffusion diffusion models generative generative modeling math.ds math.pr modeling process processes results space space and time spaces state stat.ml stochastic study type understanding via work