mlsanityData to 14 Oct 2026

The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space

arXiv 2606.01847 ↗First posted 1 Jun 2026cs.RO cs.LGcited by 0

On the map: Vision-language-action models → 3D and spatial-aware VLA

Abstract (arXiv)

Diffusion-based Vision-Language-Action policies achieve remarkable success in robotic manipulation, yet commit a fundamental geometric error we term the Euclidean Fallacy: representing SE(3) poses as flat ℝ12 vectors. This approximation induces (1) manifold drift violating SO(3) constraints, (2) broken equivariance under coordinate transformations, and (3) non-geodesic trajectories with excessive kinematic cost. We introduce Lie Diffuser Actor (LDA), a diffusion framework operating intrinsically on SE(3). Our method injects noise through left-invariant SDEs, predicts scores in the tangent space, and retracts samples via the exponential map. This formulation eliminates manifold drift by construction while guaranteeing coordinate-frame equivariance and geodesic optimality. On CALVIN ABCrightarrowD, LDA improves average task length from 3.27 to 3.51 (+7.3%). We further validate our method on real robot and the results show that our methodology outperforms the baseline on majority tasks.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in 3D and spatial-aware VLA, one of 13 directions in Vision-language-action models. Builds on 37 of its 40 references that are in the map. First posted on arXiv 1 Jun 2026.

Builds on

37 of 40 references.

Closest ancestors · 1

Same direction, newest first

  1. 2025SpatialVLA: Exploring Spatial Representations for Visual-Language-Action Model27 Jan

Other references · 36

  1. 2017Attention Is All You Needcited by 60,361
  2. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
  3. 2017Graph Attention Networkscited by 8,923
  4. 2023RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Controlcited by 3,080
  5. 2024OpenVLA: An Open-Source Vision-Language-Action Modelcited by 2,887
  6. 2023Diffusion Policy: Visuomotor Policy Learning via Action Diffusioncited by 2,838
  7. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,434
  8. 2024π0: A Vision-Language-Action Flow Model for General Robot Controlcited by 2,407
  9. 2022RT-1: Robotics Transformer for Real-World Control at Scalecited by 2,061
  10. 2025π0.5: a Vision-Language-Action Model with Open-World Generalizationcited by 1,761
  11. 2025GR00T N1: An Open Foundation Model for Generalist Humanoid Robotscited by 1,225
  12. 2025Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Successcited by 883
24 more
  1. 2024RDT-1B: a Diffusion Foundation Model for Bimanual Manipulationcited by 691
  2. 2021CALVIN: A Benchmark for Language-Conditioned Policy Learning for Long-Horizon Robot Manipulation Taskscited by 584
  3. 2024CogACT: A Foundational Vision-Language-Action Model for Synergizing Cognition and Action in Robotic Manipulationcited by 422
  4. 2024Universal Manipulation Interface: In-The-Wild Robot Teaching Without In-The-Wild Robotscited by 394
  5. 2025WorldVLA: Towards Autoregressive Action World Modelcited by 367
  6. 20243D Diffuser Actor: Policy Diffusion with 3D Scene Representationscited by 282
  7. 2023Flow Matching on General Geometriescited by 265
  8. 2022Riemannian Score-Based Generative Modellingcited by 219
  9. 2025HybridVLA: Collaborative Diffusion and Autoregression in a Unified Vision-Language-Action Modelcited by 181
  10. 2025ThinkAct: Vision-Language-Action Reasoning via Reinforced Visual Latent Planningcited by 156
  11. 2022SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusioncited by 127
  12. 2025GR-3 Technical Reportcited by 111
  13. 2025OpenHelix: A Short Survey, Empirical Analysis, and Open-Source Dual-System VLA Model for Robotic Manipulationcited by 82
  14. 2024EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learningcited by 75
  15. 2022Theseus: A Library for Differentiable Nonlinear Optimizationcited by 65
  16. 2024Riemannian Flow Matching Policy for Robot Motion Learningcited by 63
  17. 2025villa-X: Enhancing Latent Action Modeling in Vision-Language-Action Modelscited by 63
  18. 2024Diffusion-VLA: Generalizable and Interpretable Robot Foundation Model via Self-Generated Reasoningcited by 57
  19. 2025VTLA: Vision-Tactile-Language-Action Model with Preference Learning for Insertion Manipulationcited by 55
  20. 2023Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulationcited by 52
  21. 2024ET-SEED: Efficient Trajectory-Level SE(3) Equivariant Diffusion Policycited by 26
  22. 2025Diffusion Generative Modeling on Lie Group Representationscited by 8
  23. 2025SE(3)-Equivariant Diffusion Policy in Spherical Fourier Spacecited by 8
  24. 2025Parallel Sampling of Diffusion Models on SO(3)cited by 1

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