# How Well do Diffusion Policies Learn Kinematic Constraint Manifolds?

arXiv: https://arxiv.org/abs/2510.01404 · HTML: https://mlsanity.com/paper/2510.01404/

## Key facts

- Cited by 3 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 27 of its 40 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## 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, 27 of 27)

- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [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)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Riemannian Score-Based Generative Modelling](https://mlsanity.com/paper/2202.02763/) (2022)
- [A Careful Examination of Large Behavior Models for Multitask Dexterous Manipulation](https://mlsanity.com/paper/2507.05331/) (2025)
- [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022)
- [Does data interpolation contradict statistical optimality?](https://mlsanity.com/paper/1806.09471/) (2018)
- [Diffusion Models for Constrained Domains](https://mlsanity.com/paper/2304.05364/) (2023)
- [PoCo: Policy Composition from and for Heterogeneous Robot Learning](https://mlsanity.com/paper/2402.02511/) (2024)
- [Diffusion Models for Robotic Manipulation: A Survey](https://mlsanity.com/paper/2504.08438/) (2025)
- [Movement Primitive Diffusion: Learning Gentle Robotic Manipulation of Deformable Objects](https://mlsanity.com/paper/2312.10008/) (2023)
- [Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior](https://mlsanity.com/paper/2307.14619/) (2023)
- [Diffusion Predictive Control with Constraints](https://mlsanity.com/paper/2412.09342/) (2024)
- [Metropolis Sampling for Constrained Diffusion Models](https://mlsanity.com/paper/2307.05439/) (2023)
- [On the Role of the Action Space in Robot Manipulation Learning and Sim-to-Real Transfer](https://mlsanity.com/paper/2312.03673/) (2023)
- [Interpreting and Improving Diffusion Models from an Optimization Perspective](https://mlsanity.com/paper/2306.04848/) (2023)
- [A Comparison of Action Spaces for Learning Manipulation Tasks](https://mlsanity.com/paper/1908.08659/) (2019)
- [Empirical Analysis of Sim-and-Real Cotraining of Diffusion Policies for Planar Pushing from Pixels](https://mlsanity.com/paper/2503.22634/) (2025)
- [Constraint-Aware Diffusion Models for Trajectory Optimization](https://mlsanity.com/paper/2406.00990/) (2024)
- [Joint Model-based Model-free Diffusion for Planning with Constraints](https://mlsanity.com/paper/2509.08775/) (2025)
- [Redundancy-aware Action Spaces for Robot Learning](https://mlsanity.com/paper/2406.04144/) (2024)
- [Redundancy parameterization and inverse kinematics of 7-DOF revolute manipulators](https://mlsanity.com/paper/2307.13122/) (2023)

## Built on by (most cited first, 3 of 3)

- [Ambient Diffusion Policy: Imitation Learning from Suboptimal Data in Robotics](https://mlsanity.com/paper/2606.12365/) (2026)
- [Exploring the Intrinsic Geometry of Diffusion Models with Constrained Inverse Kinematics](https://mlsanity.com/paper/2606.26408/) (2026)
- [Manifold-Stable Flow Matching](https://mlsanity.com/paper/2609.35454/) (2026)

## Abstract (arXiv)

Diffusion policies have shown impressive results in robot imitation learning, even for tasks that require satisfaction of kinematic equality constraints. However, task performance alone is not a reliable indicator of the policy's ability to precisely learn constraints in the training data. To investigate, we analyze how well diffusion policies discover these manifolds with a case study on a bimanual pick-and-place task that encourages fulfillment of a kinematic constraint for success. We study how three factors affect trained policies: dataset size, dataset quality, and manifold curvature. Our experiments show diffusion policies learn a coarse approximation of the constraint manifold with learning affected negatively by decreases in both dataset size and quality. On the other hand, the curvature of the constraint manifold showed inconclusive correlations with both constraint satisfaction and task success. A hardware evaluation verifies the applicability of our results in the real world. Project website with additional results and visuals: https://diffusion-learns-kinematic.github.io