# SafeDiffuser: Safe Planning with Diffusion Probabilistic Models

arXiv: https://arxiv.org/abs/2306.00148 · HTML: https://mlsanity.com/paper/2306.00148/

## Key facts

- Cited by 75 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 29 of its 50 references that are in the map.
- First posted on arXiv 31 May 2023.

## 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, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Model-Based Reinforcement Learning for Atari](https://mlsanity.com/paper/1903.00374/) (2019)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [TransDreamer: Reinforcement Learning with Transformer World Models](https://mlsanity.com/paper/2202.09481/) (2022)
- [3D Neural Scene Representations for Visuomotor Control](https://mlsanity.com/paper/2107.04004/) (2021)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Constrained Decision Transformer for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2302.07351/) (2023)
- [Vector Quantized Models for Planning](https://mlsanity.com/paper/2106.04615/) (2021)
- [Mismatched No More: Joint Model-Policy Optimization for Model-Based RL](https://mlsanity.com/paper/2110.02758/) (2021)
- [Model-based Reinforcement Learning for Semi-Markov Decision Processes with Neural ODEs](https://mlsanity.com/paper/2006.16210/) (2020)
- [Control Barrier Functions for Systems with High Relative Degree](https://mlsanity.com/paper/1903.04706/) (2019)
- [Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs](https://mlsanity.com/paper/2009.01196/) (2020)
- [Learning Accurate Long-term Dynamics for Model-based Reinforcement Learning](https://mlsanity.com/paper/2012.09156/) (2020)
- [Learning Safe Neural Network Controllers with Barrier Certificates](https://mlsanity.com/paper/2009.09826/) (2020)
- [ShieldNN: A Provably Safe NN Filter for Unsafe NN Controllers](https://mlsanity.com/paper/2006.09564/) (2020)
- [On the Forward Invariance of Neural ODEs](https://mlsanity.com/paper/2210.04763/) (2022)

## Built on by (most cited first, 30 of 75)

- [Diffusion Models for Reinforcement Learning: A Survey](https://mlsanity.com/paper/2311.01223/) (2023)
- [DiffuseLoco: Real-Time Legged Locomotion Control with Diffusion from Offline Datasets](https://mlsanity.com/paper/2404.19264/) (2024)
- [What Makes a Good Diffusion Planner for Decision Making?](https://mlsanity.com/paper/2503.00535/) (2025)
- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)
- [CGD: Constraint-Guided Diffusion Policies for UAV Trajectory Planning](https://mlsanity.com/paper/2405.01758/) (2024)
- [Dexterous Manipulation through Imitation Learning: A Survey](https://mlsanity.com/paper/2504.03515/) (2025)
- [Deep Generative Models for Offline Policy Learning: Tutorial, Survey, and Perspectives on Future Directions](https://mlsanity.com/paper/2402.13777/) (2024)
- [DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization](https://mlsanity.com/paper/2403.05571/) (2024)
- [Diffusion Model for Planning: A Systematic Literature Review](https://mlsanity.com/paper/2408.10266/) (2024)
- [LTLDoG: Satisfying Temporally-Extended Symbolic Constraints for Safe Diffusion-based Planning](https://mlsanity.com/paper/2405.04235/) (2024)
- [Generative Models in Decision Making: A Survey](https://mlsanity.com/paper/2502.17100/) (2025)
- [FlowMP: Learning Motion Fields for Robot Planning with Conditional Flow Matching](https://mlsanity.com/paper/2503.06135/) (2025)
- [DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectories](https://mlsanity.com/paper/2502.15043/) (2025)
- [SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions](https://mlsanity.com/paper/2509.24243/) (2025)
- [Constraint-Aware Diffusion Guidance for Robotics: Real-Time Obstacle Avoidance for Autonomous Racing](https://mlsanity.com/paper/2505.13131/) (2025)
- [HardFlow: Hard-Constrained Sampling for Flow-Matching Models via Trajectory Optimization](https://mlsanity.com/paper/2511.08425/) (2025)
- [OASIS: Conditional Distribution Shaping for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2407.14653/) (2024)
- [Constrained Diffusers for Safe Planning and Control](https://mlsanity.com/paper/2506.12544/) (2025)
- [Denoising Heat-inspired Diffusion with Insulators for Collision Free Motion Planning](https://mlsanity.com/paper/2310.12609/) (2023)
- [Learning from Random Demonstrations: Offline Reinforcement Learning with Importance-Sampled Diffusion Models](https://mlsanity.com/paper/2405.19878/) (2024)
- [Stable Continual Reinforcement Learning via Diffusion-based Trajectory Replay](https://mlsanity.com/paper/2411.10809/) (2024)
- [BiRoDiff: Diffusion policies for bipedal robot locomotion on unseen terrains](https://mlsanity.com/paper/2407.05424/) (2024)
- [The Duality of Generative AI and Reinforcement Learning in Robotics: A Review](https://mlsanity.com/paper/2410.16411/) (2024)
- [Zero-Shot Trajectory Planning for Signal Temporal Logic Tasks](https://mlsanity.com/paper/2501.13457/) (2025)
- [CHD: Coupled Hierarchical Diffusion for Long-Horizon Tasks](https://mlsanity.com/paper/2505.07261/) (2025)
- [Safety-Guided Flow (SGF): A Unified Framework for Negative Guidance in Safe Generation](https://mlsanity.com/paper/2603.13300/) (2026)
- [RAIL: Reachability-Aided Imitation Learning for Safe Policy Execution](https://mlsanity.com/paper/2409.19190/) (2024)
- [UniConFlow: A Unified Constrained Flow-Matching Framework for Certified Motion Planning](https://mlsanity.com/paper/2506.02955/) (2025)
- [From Demonstrations to Safe Deployment: Path-Consistent Safety Filtering for Diffusion Policies](https://mlsanity.com/paper/2511.06385/) (2025)

## Abstract (arXiv)

Diffusion model-based approaches have shown promise in data-driven planning, but there are no safety guarantees, thus making it hard to be applied for safety-critical applications. To address these challenges, we propose a new method, called SafeDiffuser, to ensure diffusion probabilistic models satisfy specifications by using a class of control barrier functions. The key idea of our approach is to embed the proposed finite-time diffusion invariance into the denoising diffusion procedure, which enables trustworthy diffusion data generation. Moreover, we demonstrate that our finite-time diffusion invariance method through generative models not only maintains generalization performance but also creates robustness in safe data generation. We test our method on a series of safe planning tasks, including maze path generation, legged robot locomotion, and 3D space manipulation, with results showing the advantages of robustness and guarantees over vanilla diffusion models.