# DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectories

arXiv: https://arxiv.org/abs/2502.15043 · HTML: https://mlsanity.com/paper/2502.15043/

## Key facts

- Cited by 14 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 41 of its 60 references that are in the map.
- First posted on arXiv 20 Feb 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 41)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [Robot Operating System 2: Design, Architecture, and Uses In The Wild](https://mlsanity.com/paper/2211.07752/) (2022)
- [Guided Conditional Diffusion for Controllable Traffic Simulation](https://mlsanity.com/paper/2210.17366/) (2022)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [AdaptDiffuser: Diffusion Models as Adaptive Self-evolving Planners](https://mlsanity.com/paper/2302.01877/) (2023)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [Reflected Diffusion Models](https://mlsanity.com/paper/2304.04740/) (2023)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Diffusion Models for Constrained Domains](https://mlsanity.com/paper/2304.05364/) (2023)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [EDMP: Ensemble-of-costs-guided Diffusion for Motion Planning](https://mlsanity.com/paper/2309.11414/) (2023)

## Built on by (most cited first, 14 of 14)

- [HardFlow: Hard-Constrained Sampling for Flow-Matching Models via Trajectory Optimization](https://mlsanity.com/paper/2511.08425/) (2025)
- [AdaWorldPolicy: World-Model-Driven Diffusion Policy with Online Adaptive Learning for Robotic Manipulation](https://mlsanity.com/paper/2602.20057/) (2026)
- [Dynamics-aware Diffusion Models for Planning and Control](https://mlsanity.com/paper/2504.00236/) (2025)
- [SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planning](https://mlsanity.com/paper/2511.05355/) (2025)
- [Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilization](https://mlsanity.com/paper/2509.19688/) (2025)
- [DiRecT: Safe Diffusion-Based Planning via Receding-Horizon Denoising](https://mlsanity.com/paper/2606.15359/) (2026)
- [X-Safe: Embodiment-Agnostic Safeguarding for Robot Arm Manipulation Policies via Action Masking](https://mlsanity.com/paper/2606.22278/) (2026)
- [CofactVLA: Deconfounding Vision-Language-Action Models via Counterfactual Intervention](https://mlsanity.com/paper/2608.04396/) (2026)
- [Belief-Conditioned One-Step Diffusion: Real-Time Trajectory Planning with Just-Enough Sensing](https://mlsanity.com/paper/2508.12166/) (2025)
- [PAD-TRO: Projection-Augmented Diffusion for Direct Trajectory Optimization](https://mlsanity.com/paper/2510.04436/) (2025)
- [Safer Trajectory Planning with CBF-guided Diffusion Model for Unmanned Aerial Vehicles](https://mlsanity.com/paper/2604.17527/) (2026)
- [Machine Unlearning for Masked Diffusion Language Models](https://mlsanity.com/paper/2605.18253/) (2026)
- [Conflict-Aware Additive Guidance for Flow Models under Compositional Rewards](https://mlsanity.com/paper/2605.20758/) (2026)
- [Manifold-Stable Flow Matching](https://mlsanity.com/paper/2609.35454/) (2026)

## Abstract (arXiv)

Diffusion models excel at creating images and videos thanks to their multimodal generative capabilities. These same capabilities have made diffusion models increasingly popular in robotics research, where they are used for generating robot motion. However, the stochastic nature of diffusion models is fundamentally at odds with the precise dynamical equations describing the feasible motion of robots. Hence, generating dynamically admissible robot trajectories is a challenge for diffusion models. To alleviate this issue, we introduce DDAT: Diffusion policies for Dynamically Admissible Trajectories to generate provably admissible trajectories of black-box robotic systems using diffusion models. A sequence of states is a dynamically admissible trajectory if each state of the sequence belongs to the reachable set of its predecessor by the robot's equations of motion. To generate such trajectories, our diffusion policies project their predictions onto a dynamically admissible manifold during both training and inference to align the objective of the denoiser neural network with the dynamical admissibility constraint. The auto-regressive nature of these projections along with the black-box nature of robot dynamics render these projections immensely challenging. We thus enforce admissibility by iteratively sampling a polytopic under-approximation of the reachable set of a state onto which we project its predicted successor, before iterating this process with the projected successor. By producing accurate trajectories, this projection eliminates the need for diffusion models to continually replan, enabling one-shot long-horizon trajectory planning. We demonstrate that our framework generates higher quality dynamically admissible robot trajectories through extensive simulations on a quadcopter and various MuJoCo environments, along with real-world experiments on a Unitree GO1 and GO2.