Constrained Generative Modeling with Manually Bridged Diffusion Models

TL;DR

This paper introduces a new framework called manual bridges for diffusion-based generative modeling on constrained spaces, allowing multiple constraints to be incorporated simultaneously while maintaining mathematical validity and practical applicability.

Contribution

The paper presents a novel manual bridge framework for constrained diffusion modeling, including mechanisms for combining multiple constraints and training models that respect these constraints and data distribution.

Findings

Successfully models constrained trajectory initializations for autonomous vehicles.

Extends diffusion theory to accommodate multiple constraints.

Demonstrates practical effectiveness in path planning tasks.

Abstract

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.