mlsanityData to 14 Oct 2026

Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Models

arXiv 2306.15512 ↗First posted 27 Jun 2023cs.ROcited by 13

On the map: Diffusion models → Diffusion and flow policies for robotics

Abstract (arXiv)

We present a framework for safety-critical optimal control of physical systems based on denoising diffusion probabilistic models (DDPMs). The technology of control barrier functions (CBFs), encoding desired safety constraints, is used in combination with DDPMs to plan actions by iteratively denoising trajectories through a CBF-based guided sampling procedure. At the same time, the generated trajectories are also guided to maximize a future cumulative reward representing a specific task to be optimally executed. The proposed scheme can be seen as an offline and model-based reinforcement learning algorithm resembling in its functionalities a model-predictive control optimization scheme with receding horizon in which the selected actions lead to optimal and safe trajectories.

Key facts. Cited by 13 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 23 of its 33 references that are in the map. First posted on arXiv 27 Jun 2023.

Builds on

23 of 33 references.

References · 23

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  6. 2022Generative Adversarial Networkscited by 5,627
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  8. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
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11 more
  1. 2019Model-Based Reinforcement Learning for Ataricited by 502
  2. 2019Control Barrier Functions: Theory and Applicationscited by 372
  3. 2017Deep Reinforcement Learning: An Overviewcited by 333
  4. 2019End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Taskscited by 289
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  6. 2022Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methodscited by 151
  7. 2020Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Functioncited by 49
  8. 2021Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learningcited by 27
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 5; 2025: 6; 2026: 1.

13 papers.

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  1. 2024DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimizationcited by 20
  2. 2024Diffusion Model for Planning: A Systematic Literature Reviewcited by 17
  3. 2024LTLDoG: Satisfying Temporally-Extended Symbolic Constraints for Safe Diffusion-based Planningcited by 16
  4. 2025DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectoriescited by 14
  5. 2023Amortized Global Search for Efficient Preliminary Trajectory Design with Deep Generative Modelscited by 12
  6. 2024Constraint-Aware Diffusion Models for Trajectory Optimizationcited by 11
  7. 2025Constraint-Aware Diffusion Guidance for Robotics: Real-Time Obstacle Avoidance for Autonomous Racingcited by 11
  8. 2025Aligning Diffusion Model with Problem Constraints for Trajectory Optimizationcited by 7
  9. 2025Zero-Shot Trajectory Planning for Signal Temporal Logic Taskscited by 6
  10. 2025SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planningcited by 3
  11. 2026Constraint-Aware Flow Matching: Decision Aligned End-to-End Training for Constrained Samplingcited by 3
  12. 2024Denoising Diffusion Planner: Learning Complex Paths from Low-Quality Demonstrationscited by 2
1 more
  1. 2025Diffusion-Based Forecasting for Uncertainty-Aware Model Predictive Controlcited by 2

Similar, not cited

Close in wording, no citation either way

  1. 2026DiRecT: Safe Diffusion-Based Planning via Receding-Horizon Denoising
  2. 2025Dynamics-aware Diffusion Models for Planning and Control
  3. 2024Denoising Diffusion-Based Control of Nonlinear Systems
  4. 2026A Control Barrier Function-Constrained Model Predictive Control Framework for Safe Reinforcement Learning
  5. 2026D-SafeMPC: Diffusion-Driven Safe Model Predictive Control with Discrete-Time Control Barrier Functions
  6. 2025Probabilistically safe and efficient model-based reinforcement learning
  7. 2026Safer Trajectory Planning with CBF-guided Diffusion Model for Unmanned Aerial Vehicles
  8. 2026Reachability-Aware Diffusion Policy Optimization