# Training-Free Imitation Learning with Closed-Form Diffusion Policies

arXiv: https://arxiv.org/abs/2606.01238 · HTML: https://mlsanity.com/paper/2606.01238/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 26 of its 30 references that are in the map.
- First posted on arXiv 31 May 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

## Builds on (most cited first, 26 of 26)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [An analytic theory of creativity in convolutional diffusion models](https://mlsanity.com/paper/2412.20292/) (2024)
- [Closed-Form Diffusion Models](https://mlsanity.com/paper/2310.12395/) (2023)
- [DynaGuide: Steering Diffusion Polices with Active Dynamic Guidance](https://mlsanity.com/paper/2506.13922/) (2025)
- [CleanDiffuser: An Easy-to-use Modularized Library for Diffusion Models in Decision Making](https://mlsanity.com/paper/2406.09509/) (2024)
- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)
- [Full-Order Sampling-Based MPC for Torque-Level Locomotion Control via Diffusion-Style Annealing](https://mlsanity.com/paper/2409.15610/) (2024)
- [DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization](https://mlsanity.com/paper/2403.05571/) (2024)
- [Selective Underfitting in Diffusion Models](https://mlsanity.com/paper/2510.01378/) (2025)
- [Stage-wise Dynamics of Classifier-Free Guidance in Diffusion Models](https://mlsanity.com/paper/2509.22007/) (2025)
- [Constraint-Aware Diffusion Models for Trajectory Optimization](https://mlsanity.com/paper/2406.00990/) (2024)
- [Demystifying Diffusion Policies: Action Memorization and Simple Lookup Table Alternatives](https://mlsanity.com/paper/2505.05787/) (2025)
- [Toward Near-Globally Optimal Nonlinear Model Predictive Control via Diffusion Models](https://mlsanity.com/paper/2412.08278/) (2024)
- [EB-MBD: Emerging-Barrier Model-Based Diffusion for Safe Trajectory Optimization in Highly Constrained Environments](https://mlsanity.com/paper/2510.07700/) (2025)

## Abstract (arXiv)

While diffusion-based policies have impressive performance and expressivity, their long offline training slows down the data collection and policy deployment loop. We introduce Closed-Form Diffusion Policies, a class of training-free diffusion-based policies for imitation learning using the closed-form score derived from the demonstration dataset. We deploy CFDP with real-time inference with a mobile CPU in hardware experiments, showing it can successfully perform imitation directly from the dataset in milliseconds and with faster inference than neural diffusion policies. In experiments on imitation learning benchmarks, we show that CFDP is competitive against neural baselines that require hours of training, providing a favorable tradeoff between training time and performance. Finally, we show how closed-form diffusion policies act as a composable primitive that enables data-driven inference-time editing of pre-trained neural diffusion policies, including policy guidance and novel demonstration augmentation.