Aligning Diffusion Model with Problem Constraints for Trajectory Optimization

2025-04-01

AI Summary

Diffusion models for trajectory optimization often violate critical constraints—including goal reaching, obstacle avoidance, and dynamical feasibility—due to their purely data-driven training, which lacks explicit integration of physical and task-specific constraints. To address this, we propose a constraint-aligned diffusion modeling paradigm inspired by Dynamic Data-Driven Application Systems (DDDAS), explicitly modeling and penalizing constraint violations during training. Our approach introduces a novel step-wise statistical modeling of constraint violations across the diffusion process, coupled with a violation-aware reweighting strategy, and a hybrid loss function that jointly incorporates physics-based constraints to co-optimize trajectory quality and feasibility. Experiments on robotic tabletop manipulation and dual-vehicle reach-avoid tasks demonstrate substantial reductions in constraint violation rates while preserving trajectory diversity and smoothness, enabling real-time, online adaptive planning.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Diffusion models have recently emerged as effective generative frameworks for trajectory optimization, capable of producing high-quality and diverse solutions. However, training these models in a purely data-driven manner without explicit incorporation of constraint information often leads to violations of critical constraints, such as goal-reaching, collision avoidance, and adherence to system dynamics. To address this limitation, we propose a novel approach that aligns diffusion models explicitly with problem-specific constraints, drawing insights from the Dynamic Data-driven Application Systems (DDDAS) framework. Our approach introduces a hybrid loss function that explicitly measures and penalizes constraint violations during training. Furthermore, by statistically analyzing how constraint violations evolve throughout the diffusion steps, we develop a re-weighting strategy that aligns predicted violations to ground truth statistics at each diffusion step. Evaluated on a tabletop manipulation and a two-car reach-avoid problem, our constraint-aligned diffusion model significantly reduces constraint violations compared to traditional diffusion models, while maintaining the quality of trajectory solutions. This approach is well-suited for integration into the DDDAS framework for efficient online trajectory adaptation as new environmental data becomes available.

Problem

• Aligns diffusion models with trajectory optimization constraints
• Reduces violations like collision avoidance and goal-reaching
• Integrates DDDAS for online trajectory adaptation

Innovation

• Hybrid loss function penalizes constraint violations
• Re-weighting strategy aligns violation statistics
• Constraint-aligned diffusion model reduces violations