{"ID":2921092,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-04T07:41:34.29888543Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.01847","arxiv_id":"2606.01847","title":"The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space","abstract":"Diffusion-based Vision-Language-Action policies achieve remarkable success in robotic manipulation, yet commit a fundamental geometric error we term the $\\textbf{Euclidean Fallacy}$: representing SE(3) poses as flat $\\mathbb{R}^{12}$ 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 $\\textbf{Lie Diffuser Actor (LDA)}$, 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 ABC$\\rightarrow$D, 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.","short_abstract":"Diffusion-based Vision-Language-Action policies achieve remarkable success in robotic manipulation, yet commit a fundamental geometric error we term the $\\textbf{Euclidean Fallacy}$: representing SE(3) poses as flat $\\mathbb{R}^{12}$ vectors. This approximation induces (1) manifold drift violating SO(3) constraints, (2...","url_abs":"https://arxiv.org/abs/2606.01847","url_pdf":"https://arxiv.org/pdf/2606.01847v1","authors":"[\"Bing-Cheng Chuang\",\"I-Hsuan Chu\",\"Bor-Jiun Lin\",\"YuanFu Yang\",\"Min Sun\",\"Chun-Yi Lee\"]","published":"2026-06-01T07:59:29Z","proceeding":"cs.RO","tasks":"[\"cs.RO\",\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}