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keywords:
ml
autoencoders
deep generative models
In this paper we describe a novel framework for diffusion-based generative modeling on constrained spaces. In particular we expand 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 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 one particular high-value application in modeling trajectory initializations for path planning and control in autonomous vehicles.
