# Making two action heads agree: coordination mechanisms and a runtime collapse certificate for flow-matching policies

arXiv: https://arxiv.org/abs/2608.15748 · HTML: https://mlsanity.com/paper/2608.15748/

## 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 23 of its 49 references that are in the map.
- First posted on arXiv 16 Aug 2026.

## 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, 23 of 23)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [SyncDreamer: Generating Multiview-consistent Images from a Single-view Image](https://mlsanity.com/paper/2309.03453/) (2023)
- [LIBERO-Plus: In-depth Robustness Analysis of Vision-Language-Action Models](https://mlsanity.com/paper/2510.13626/) (2025)
- [EnsembleDAgger: A Bayesian Approach to Safe Imitation Learning](https://mlsanity.com/paper/1807.08364/) (2018)
- [Hierarchical Diffusion Policy for Kinematics-Aware Multi-Task Robotic Manipulation](https://mlsanity.com/paper/2403.03890/) (2024)
- [Can We Detect Failures Without Failure Data? Uncertainty-Aware Runtime Failure Detection for Imitation Learning Policies](https://mlsanity.com/paper/2503.08558/) (2025)
- [Failure Prediction at Runtime for Generative Robot Policies](https://mlsanity.com/paper/2510.09459/) (2025)
- [Diff-DAgger: Uncertainty Estimation with Diffusion Policy for Robotic Manipulation](https://mlsanity.com/paper/2410.14868/) (2024)
- [Wasserstein Task Embedding for Measuring Task Similarities](https://mlsanity.com/paper/2208.11726/) (2022)
- [Implicit Kinematic Policies: Unifying Joint and Cartesian Action Spaces in End-to-End Robot Learning](https://mlsanity.com/paper/2203.01983/) (2022)
- [Demystifying Action Space Design for Robotic Manipulation Policies](https://mlsanity.com/paper/2602.23408/) (2026)
- [Hide-and-Seek in Trajectories: Discovering Failure Signals for VLA Runtime Monitoring](https://mlsanity.com/paper/2605.30834/) (2026)
- [Hierarchical Rectified Flow Matching with Mini-Batch Couplings](https://mlsanity.com/paper/2507.13350/) (2025)
- [Shifting Uncertainty to Critical Moments: Towards Reliable Uncertainty Quantification for VLA Model](https://mlsanity.com/paper/2603.18342/) (2026)
- [Uncertainty Quantification for Flow-Based Vision-Language-Action Models](https://mlsanity.com/paper/2606.18043/) (2026)
- [NoiseController: Towards Consistent Multi-view Video Generation via Noise Decomposition and Collaboration](https://mlsanity.com/paper/2504.18448/) (2025)
- [ActProbe: Action-Space Probe for Early Failure Detection of Generative Robot Policies](https://mlsanity.com/paper/2606.08508/) (2026)
- [Couple to Control: Joint Initial Noise Design in Diffusion Models](https://mlsanity.com/paper/2605.11311/) (2026)
- [MimicIK: Real-Time Generative Inverse Kinematics from Teleoperation with FK Consistency](https://mlsanity.com/paper/2606.15148/) (2026)
- [Kolmogorov n-Widths for Multitask Physics-Informed Machine Learning (PIML) Methods: Towards Robust Metrics](https://mlsanity.com/paper/2402.11126/) (2024)
- [Mixture of Frames Policy: Multi-Frame Action Denoising for Bimanual Mobile Manipulation](https://mlsanity.com/paper/2607.11884/) (2026)

## Abstract (arXiv)

A dual-representation flow-matching policy decodes each predicted motion into joint and end-effector spaces, and the residual between the two kinematically equivalent decodings provides a physically interpretable runtime signal. On multimodal tasks, however, independently sampled branches may choose different valid modes, causing false alarms. We study how to coordinate the two branches and at what cost. Across two robot environments and a non-robotic testbed, the tested mechanisms fall into four classes. An auxiliary latent shared by both branches but absent from the flow-matching construction is erased at the population optimum, a provable dead end confirmed within a prespecified 2% equivalence band. Sharing source noise can coordinate or anti-coordinate: its effect changes sign with the representation map and tracks the alignment of decoder mode basins. Consistency regularization gives intermediate coordination but reduces the valid-pair rate, while training-supported discrete partitions achieve near-ceiling coordination robustly. We further derive a chance-corrected coordination bound based only on each branch's Gini-Simpson diversity, yielding an attainable region and a label-free certificate that separates coordination from collapse when zero mismatch is ambiguous. On LIBERO-Plus, benign multimodality adds 1.57 percentage points of false alarms to the residual, which remains the strongest evaluated failure signal; the preregistered token intervention does not meet its false-alarm criterion or produce a seed-robust detection change. Code, models, and per-run configurations are available at https://github.com/kimo423/dual-head-coordination.