Constrained Generative Modeling with Manually Bridged Diffusion Models

2025-02-27

AI Summary

Modeling diffusion-based generation under multiple hard constraints (e.g., kinematics, environment) in safety-critical, resource-constrained settings remains challenging. Method: We propose Manual Bridging—a theoretically grounded framework that enables joint embedding and strict satisfaction of heterogeneous hard constraints. We prove it constructs a valid diffusion bridge, ensuring probability flow consistency and constraint completeness; further, we introduce a distribution alignment training strategy to precisely match the data distribution within the constrained space. Contribution/Results: This is the first application of constrained diffusion models to autonomous driving trajectory initialization. Generated trajectories satisfy *all* hard constraints with 100% fidelity; path success rate improves by 23% over SOTA baselines, while feasibility and trajectory diversity are significantly enhanced. Our work establishes a new paradigm for high-reliability generative modeling—rigorous in theory and practical in deployment.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Diffusion-based generative modeling on constrained spaces
• Combining multiple constraints in diffusion models
• Training models for autonomous vehicle path planning

Innovation

• Manual bridges expand constraint types
• Mechanism combines multiple constraints effectively
• Training adapts to data distribution precisely