# Diffusion Predictive Control with Constraints

arXiv: https://arxiv.org/abs/2412.09342 · HTML: https://mlsanity.com/paper/2412.09342/

## Key facts

- Cited by 33 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 21 of its 30 references that are in the map.
- First posted on arXiv 12 Dec 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, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (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)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Imitating Human Behaviour with Diffusion Models](https://mlsanity.com/paper/2301.10677/) (2023)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [Towards Diverse Behaviors: A Benchmark for Imitation Learning with Human Demonstrations](https://mlsanity.com/paper/2402.14606/) (2024)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [PlayFusion: Skill Acquisition via Diffusion from Language-Annotated Play](https://mlsanity.com/paper/2312.04549/) (2023)
- [DiffuseLoco: Real-Time Legged Locomotion Control with Diffusion from Offline Datasets](https://mlsanity.com/paper/2404.19264/) (2024)
- [Diffusion Model Predictive Control](https://mlsanity.com/paper/2410.05364/) (2024)
- [Deep Generative Models in Robotics: A Survey on Learning from Multimodal Demonstrations](https://mlsanity.com/paper/2408.04380/) (2024)
- [CGD: Constraint-Guided Diffusion Policies for UAV Trajectory Planning](https://mlsanity.com/paper/2405.01758/) (2024)

## Built on by (most cited first, 30 of 33)

- [Diffusion Models for Robotic Manipulation: A Survey](https://mlsanity.com/paper/2504.08438/) (2025)
- [Diffuse-CLoC: Guided Diffusion for Physics-based Character Look-ahead Control](https://mlsanity.com/paper/2503.11801/) (2025)
- [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)
- [HardFlow: Hard-Constrained Sampling for Flow-Matching Models via Trajectory Optimization](https://mlsanity.com/paper/2511.08425/) (2025)
- [Projected Coupled Diffusion for Test-Time Constrained Joint Generation](https://mlsanity.com/paper/2508.10531/) (2025)
- [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)
- [Dynamics-aware Diffusion Models for Planning and Control](https://mlsanity.com/paper/2504.00236/) (2025)
- [Pick-and-place Manipulation Across Grippers Without Retraining: A Learning-optimization Diffusion Policy Approach](https://mlsanity.com/paper/2502.15613/) (2025)
- [Diffusion-Based Approximate MPC: Fast and Consistent Imitation of Multi-Modal Action Distributions](https://mlsanity.com/paper/2504.04603/) (2025)
- [How Well do Diffusion Policies Learn Kinematic Constraint Manifolds?](https://mlsanity.com/paper/2510.01404/) (2025)
- [SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planning](https://mlsanity.com/paper/2511.05355/) (2025)
- [Model-Based Diffusion Sampling for Predictive Control in Offline Decision Making](https://mlsanity.com/paper/2512.08280/) (2025)
- [Inference-stage Adaptation-projection Strategy Adapts Diffusion Policy to Cross-manipulators Scenarios](https://mlsanity.com/paper/2509.11621/) (2025)
- [PHDME: Physics-Informed Diffusion Models without Explicit Governing Equations](https://mlsanity.com/paper/2601.21234/) (2026)
- [DiRecT: Safe Diffusion-Based Planning via Receding-Horizon Denoising](https://mlsanity.com/paper/2606.15359/) (2026)
- [Grounding Generative Policies in Physics: Optimization-Guided Diffusion for Robot Control](https://mlsanity.com/paper/2606.24208/) (2026)
- [MATT-Diff: Multimodal Active Target Tracking by Diffusion Policy](https://mlsanity.com/paper/2511.11931/) (2025)
- [Warm-Starting Collision-Free Model Predictive Control With Object-Centric Diffusion](https://mlsanity.com/paper/2601.02873/) (2026)
- [Motion Planning with Model-Based Diffusion via Constraint Optimization and Adaptive Scheduling](https://mlsanity.com/paper/2607.14455/) (2026)
- [Flow-Opt: Scalable Centralized Multi-Robot Trajectory Optimization with Flow Matching and Differentiable Optimization](https://mlsanity.com/paper/2510.09204/) (2025)
- [Efficient Diffusion Models under Nonconvex Equality and Inequality constraints via Landing](https://mlsanity.com/paper/2604.17838/) (2026)
- [Conflict-Aware Additive Guidance for Flow Models under Compositional Rewards](https://mlsanity.com/paper/2605.20758/) (2026)
- [BayesFP: Posterior Estimation for Flow-Based Policies via Feynman-Kac Sampling](https://mlsanity.com/paper/2606.21014/) (2026)
- [SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling](https://mlsanity.com/paper/2607.00095/) (2026)
- [D-SafeMPC: Diffusion-Driven Safe Model Predictive Control with Discrete-Time Control Barrier Functions](https://mlsanity.com/paper/2607.10842/) (2026)
- [D-IMPL: A Diffusion-based Solver for Parameterized BBOs](https://mlsanity.com/paper/2609.22752/) (2026)
- [PredActor: Predictive Action Diffusion for Steerable Onboard Humanoid Control](https://mlsanity.com/paper/2609.24840/) (2026)
- [Steer2Grasp: Inference-Time Embodiment-Aware Steering for Diverse Physically Feasible Grasp Diffusion](https://mlsanity.com/paper/2609.33546/) (2026)

## Abstract (arXiv)

Diffusion models have become popular for policy learning in robotics due to their ability to capture high-dimensional and multimodal distributions. However, diffusion policies are stochastic and typically trained offline, limiting their ability to handle unseen and dynamic conditions where novel constraints not represented in the training data must be satisfied. To overcome this limitation, we propose diffusion predictive control with constraints (DPCC), an algorithm for diffusion-based control with explicit state and action constraints that can deviate from those in the training data. DPCC incorporates model-based projections into the denoising process of a trained trajectory diffusion model and uses constraint tightening to account for model mismatch. This allows us to generate constraint-satisfying, dynamically feasible, and goal-reaching trajectories for predictive control. We show through simulations of a robot manipulator that DPCC outperforms existing methods in satisfying novel test-time constraints while maintaining performance on the learned control task.