# CGD: Constraint-Guided Diffusion Policies for UAV Trajectory Planning

arXiv: https://arxiv.org/abs/2405.01758 · HTML: https://mlsanity.com/paper/2405.01758/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 27 of its 33 references that are in the map.
- First posted on arXiv 2 May 2024.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Learning High-Speed Flight in the Wild](https://mlsanity.com/paper/2110.05113/) (2021)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [Deep Drone Acrobatics](https://mlsanity.com/paper/2006.05768/) (2020)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [Learning Deep Control Policies for Autonomous Aerial Vehicles with MPC-Guided Policy Search](https://mlsanity.com/paper/1509.06791/) (2015)
- [Control Barrier Functions for Systems with High Relative Degree](https://mlsanity.com/paper/1903.04706/) (2019)
- [RAYEN: Imposition of Hard Convex Constraints on Neural Networks](https://mlsanity.com/paper/2307.08336/) (2023)
- [PLATO: Policy Learning using Adaptive Trajectory Optimization](https://mlsanity.com/paper/1603.00622/) (2016)
- [RAPTOR: Robust and Perception-aware Trajectory Replanning for Quadrotor Fast Flight](https://mlsanity.com/paper/2007.03465/) (2020)
- [MADER: Trajectory Planner in Multi-Agent and Dynamic Environments](https://mlsanity.com/paper/2010.11061/) (2020)
- [DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization](https://mlsanity.com/paper/2403.05571/) (2024)
- [Demonstration-Efficient Guided Policy Search via Imitation of Robust Tube MPC](https://mlsanity.com/paper/2109.09910/) (2021)
- [Deep-PANTHER: Learning-Based Perception-Aware Trajectory Planner in Dynamic Environments](https://mlsanity.com/paper/2209.01268/) (2022)
- [MINVO Basis: Finding Simplexes with Minimum Volume Enclosing Polynomial Curves](https://mlsanity.com/paper/2010.10726/) (2020)
- [PANTHER: Perception-Aware Trajectory Planner in Dynamic Environments](https://mlsanity.com/paper/2103.06372/) (2021)
- [PUMA: Fully Decentralized Uncertainty-aware Multiagent Trajectory Planner with Real-time Image Segmentation-based Frame Alignment](https://mlsanity.com/paper/2311.03655/) (2023)

## Built on by (most cited first, 21 of 21)

- [Diffusion Predictive Control with Constraints](https://mlsanity.com/paper/2412.09342/) (2024)
- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [Diffusion Model for Planning: A Systematic Literature Review](https://mlsanity.com/paper/2408.10266/) (2024)
- [DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectories](https://mlsanity.com/paper/2502.15043/) (2025)
- [Constraint-Aware Diffusion Guidance for Robotics: Real-Time Obstacle Avoidance for Autonomous Racing](https://mlsanity.com/paper/2505.13131/) (2025)
- [DiffRefiner: Coarse to Fine Trajectory Planning via Diffusion Refinement with Semantic Interaction for End to End Autonomous Driving](https://mlsanity.com/paper/2511.17150/) (2025)
- [Projected Coupled Diffusion for Test-Time Constrained Joint Generation](https://mlsanity.com/paper/2508.10531/) (2025)
- [Dynamic High-Order Control Barrier Functions with Diffuser for Safety-Critical Trajectory Planning at Signal-Free Intersections](https://mlsanity.com/paper/2412.00162/) (2024)
- [Hybrid Diffusion Policies with Projective Geometric Algebra for Efficient Robot Manipulation Learning](https://mlsanity.com/paper/2507.05695/) (2025)
- [DiffAero: A GPU-Accelerated Differentiable Simulation Framework for Efficient Quadrotor Policy Learning](https://mlsanity.com/paper/2509.10247/) (2025)
- [SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planning](https://mlsanity.com/paper/2511.05355/) (2025)
- [Self-Imitated Diffusion Policy for Efficient and Robust Visual Navigation](https://mlsanity.com/paper/2601.22965/) (2026)
- [mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks](https://mlsanity.com/paper/2502.02434/) (2025)
- [Diffusion-based learning framework for Constrained Nonconvex Optimization with Weighted Bootstrapped Refinement](https://mlsanity.com/paper/2502.10330/) (2025)
- [Diffusing Trajectory Optimization Problems for Recovery During Multi-Finger Manipulation](https://mlsanity.com/paper/2510.07030/) (2025)
- [DualShield: Safe Model Predictive Diffusion via Reachability Analysis for Interactive Autonomous Driving](https://mlsanity.com/paper/2601.15729/) (2026)
- [PRIMER: Perception-Aware Robust Learning-based Multiagent Trajectory Planner](https://mlsanity.com/paper/2406.10060/) (2024)
- [Robust Planning for Autonomous Driving via Mixed Adversarial Diffusion Predictions](https://mlsanity.com/paper/2505.12327/) (2025)
- [FlightDiffusion: Revolutionising Autonomous Drone Training with Diffusion Models Generating FPV Video](https://mlsanity.com/paper/2509.14082/) (2025)
- [ODG-NoMaD: Overhead-Camera Direction-Guided NoMaD](https://mlsanity.com/paper/2608.21395/) (2026)
- [Guiding End-to-End Driving Models with Endpoint-Constrained Trajectory Optimization](https://mlsanity.com/paper/2609.31383/) (2026)

## Abstract (arXiv)

Traditional optimization-based planners, while effective, suffer from high computational costs, resulting in slow trajectory generation. A successful strategy to reduce computation time involves using Imitation Learning (IL) to develop fast neural network (NN) policies from those planners, which are treated as expert demonstrators. Although the resulting NN policies are effective at quickly generating trajectories similar to those from the expert, (1) their output does not explicitly account for dynamic feasibility, and (2) the policies do not accommodate changes in the constraints different from those used during training. To overcome these limitations, we propose Constraint-Guided Diffusion (CGD), a novel IL-based approach to trajectory planning. CGD leverages a hybrid learning/online optimization scheme that combines diffusion policies with a surrogate efficient optimization problem, enabling the generation of collision-free, dynamically feasible trajectories. The key ideas of CGD include dividing the original challenging optimization problem solved by the expert into two more manageable sub-problems: (a) efficiently finding collision-free paths, and (b) determining a dynamically-feasible time-parametrization for those paths to obtain a trajectory. Compared to conventional neural network architectures, we demonstrate through numerical evaluations significant improvements in performance and dynamic feasibility under scenarios with new constraints never encountered during training.