Constrained Generative Modeling with Manually Bridged Diffusion Models
This addresses constrained generative modeling for applications such as autonomous vehicle path planning, representing an incremental advance in diffusion-based methods.
The paper tackles constrained generative modeling by introducing manual bridges, a framework that expands the types of constraints usable in diffusion bridges and combines multiple constraints while respecting them all. The result is a mathematically validated mechanism demonstrated in tasks like trajectory initialization for autonomous vehicles.
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.