# Constrained Diffusers for Safe Planning and Control

arXiv: https://arxiv.org/abs/2506.12544 · HTML: https://mlsanity.com/paper/2506.12544/

## Key facts

- Cited by 10 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 33 of its 52 references that are in the map.
- First posted on arXiv 14 Jun 2025.

## 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, 30 of 33)

- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem](https://mlsanity.com/paper/1802.08089/) (2018)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [Safe Offline Reinforcement Learning with Feasibility-Guided Diffusion Model](https://mlsanity.com/paper/2401.10700/) (2024)
- [Diffusion Models for Constrained Domains](https://mlsanity.com/paper/2304.05364/) (2023)
- [Efficient constrained sampling via the mirror-Langevin algorithm](https://mlsanity.com/paper/2010.16212/) (2020)
- [Sampling from a log-concave distribution with Projected Langevin Monte Carlo](https://mlsanity.com/paper/1507.02564/) (2015)
- [Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models](https://mlsanity.com/paper/2502.03607/) (2025)
- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)
- [Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space](https://mlsanity.com/paper/2202.01908/) (2022)

## Built on by (most cited first, 10 of 10)

- [How Does the Lagrangian Guide Safe Reinforcement Learning through Diffusion Models?](https://mlsanity.com/paper/2602.02924/) (2026)
- [Model-Based Diffusion Sampling for Predictive Control in Offline Decision Making](https://mlsanity.com/paper/2512.08280/) (2025)
- [Constrained Flow Optimization via Sequential Fine Tuning for Molecular Design](https://mlsanity.com/paper/2605.30610/) (2026)
- [NEGATE: Constrained Semantic Guidance for Linguistic Negation in Text-to-Video Diffusion](https://mlsanity.com/paper/2603.06533/) (2026)
- [Contractive Diffusion Policies: Robust Action Diffusion via Contractive Score-Based Sampling with Differential Equations](https://mlsanity.com/paper/2601.01003/) (2026)
- [DCR: Counterfactual Attractor Guidance for Rare Compositional Generation](https://mlsanity.com/paper/2605.06512/) (2026)
- [Decoupled Guidance Diffusion for Adaptive Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2605.02777/) (2026)
- [Towards Trustworthy Embodied Intelligence: A Systems Framework and Graded Trustworthiness Levels](https://mlsanity.com/paper/2607.26121/) (2026)
- [Safe Score Matching: Diffusion Policies with Hamilton-Jacobi Reachability for Online Safe Reinforcement Learning](https://mlsanity.com/paper/2609.33337/) (2026)
- [Reachability-Aware Diffusion Policy Optimization](https://mlsanity.com/paper/2610.05969/) (2026)

## Abstract (arXiv)

Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge for diffusion models. This paper proposes Constrained Diffusers, a novel framework that incorporates constraints into pre-trained diffusion models without retraining or architectural modifications. Inspired by constrained optimization, we apply a constrained Langevin sampling mechanism for the reverse diffusion process that jointly optimizes the trajectory and realizes constraint satisfaction through three iterative algorithms: projected method, primal-dual method and augmented Lagrangian approaches. In addition, we incorporate discrete control barrier functions as constraints for constrained diffusers to guarantee safety in online implementation. Experiments in Maze2D, locomotion, and pybullet ball running tasks demonstrate that our proposed methods achieve constraint satisfaction with less computation time, and are competitive to existing methods in environments with static and time-varying constraints.