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Aligning Diffusion Model with Problem Constraints for Trajectory Optimization

Anjian Li, Ryne Beeson

TL;DR

This work addresses constraint violations in diffusion-model-based trajectory optimization by introducing a constraint-aligned diffusion framework. The approach integrates problem constraint information into training via a hybrid loss and a re-weighting scheme grounded in ground-truth violation statistics, operating within the Dynamic Data Driven Applications Systems (DDDAS) paradigm. Evaluations on tabletop manipulation and two-car reach-avoid demonstrate significantly fewer constraint violations while preserving high-quality trajectory samples, and show compatibility with online adaptation via DDDAS. The results suggest that constraint-aware diffusion can provide feasible, efficient trajectory generation in dynamic environments, with potential for real-time deployment and continual online refinement.

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.

Aligning Diffusion Model with Problem Constraints for Trajectory Optimization

TL;DR

This work addresses constraint violations in diffusion-model-based trajectory optimization by introducing a constraint-aligned diffusion framework. The approach integrates problem constraint information into training via a hybrid loss and a re-weighting scheme grounded in ground-truth violation statistics, operating within the Dynamic Data Driven Applications Systems (DDDAS) paradigm. Evaluations on tabletop manipulation and two-car reach-avoid demonstrate significantly fewer constraint violations while preserving high-quality trajectory samples, and show compatibility with online adaptation via DDDAS. The results suggest that constraint-aware diffusion can provide feasible, efficient trajectory generation in dynamic environments, with potential for real-time deployment and continual online refinement.

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.

Paper Structure

This paper contains 20 sections, 11 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Amortized Optimization
  4. Diffusion Models.
  5. Diffusion Model with Constraints.
  6. Preliminaries
  7. Trajectory Optimization Problem
  8. Unconstrained Diffusion Model
  9. AmorGS with Diffusion Models
  10. Methodology
  11. Importance of Constraints Information
  12. Constraint-Aligned Diffusion Model
  13. Experiment
  14. Problem Setup
  15. Tabletop Manipulation
  16. ...and 5 more sections

Figures (9)

  • Figure 1: Local optimal solution structure varies with optimization problem parameter $\alpha$. Figure is adopted from beeson2024global.
  • Figure 2: Left: Unconstrained diffusion samples (red) around a local optima (star) with an infeasible region (grey) presented. Right: Constraint-aligned diffusion samples (yellow) around the same local optima.
  • Figure 3: Example trajectory for the tabletop manipulation and 2-car reach-avoid. "Obs" are short for obstacles.
  • Figure 4: Hybrid training loss computation in constraint-aligned diffusion models. "GT" denotes ground truth. "NN" denotes neural networks.
  • Figure 5: Ground truth constraint violation. Left: Tabletop Manipulation. Right: Two-car Reach-Avoid.
  • ...and 4 more figures