In this paper we describe a novel framework for diffusion-based generative modeling on constrained spaces. In particular, we introduce manual bridges, a framework that expands the kinds of constraints that can be practically used to form so-called diffusion bridges. We develop a mechanism for combining multiple such constraints so that the resulting multiply-constrained model remains a manual bridge that respects all constraints. We also develop a mechanism for training a diffusion model that respects such multiple constraints while also adapting it to match a data distribution. We develop and extend theory demonstrating the mathematical validity of our mechanisms. Additionally, we demonstrate our mechanism in constrained generative modeling tasks, highlighting a particular high-value application in modeling trajectory initializations for path planning and control in autonomous vehicles.
@article{arxiv.2502.20371,
title = {Constrained Generative Modeling with Manually Bridged Diffusion Models},
author = {Saeid Naderiparizi and Xiaoxuan Liang and Berend Zwartsenberg and Frank Wood},
journal= {arXiv preprint arXiv:2502.20371},
year = {2025}
}