Multidimensional Interpolants

arXiv:2404.14161v1 Announce Type: new
Abstract: In the domain of differential equation-based generative modeling, conventional approaches often rely on single-dimensional scalar values as interpolation coefficients during both training and inference phases. In this work, we introduce, for the first time, a multidimensional interpolant that extends these coefficients into multiple dimensions, leveraging the stochastic interpolant framework. Additionally, we propose a novel path optimization problem tailored to adaptively determine multidimensional inference trajectories, with a predetermined differential equation solver and a fixed number of …

abstract arxiv cs.ai cs.lg differential differential equation dimensions domain equation framework generative generative modeling inference interpolation modeling multidimensional multiple stochastic training type values work