{"ID":5935908,"CreatedAt":"2026-07-07T01:22:02.77346169Z","UpdatedAt":"2026-07-07T02:10:06.972658124Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.02977","arxiv_id":"2607.02977","title":"Function-Space Diffusion for Motion Planning","abstract":"Diffusion-based motion planners have demonstrated strong performance in generating diverse and high-quality robot trajectories in cluttered environments with multiple feasible solutions. However, existing approaches typically operate on fixed-length waypoint sequences, making the learned model resolution-dependent, thereby preventing zero-shot generalization across resolutions. In this work, we propose Function-Space Diffusion for Motion Planning (FSD-MP), a diffusion-based motion planner that models trajectories as continuous functions and performs diffusion directly in function space, achieving discretization-invariant trajectory generation. We define a mode-wise forward process in the spectral domain, driven by Gaussian noise with a Matérn-type covariance, and parameterize the reverse process with a boundary-compatible Discrete Sine Transform-based Fourier Neural Operator (DST-FNO) that preserves start-goal constraints across resolutions. We evaluate FSD-MP on 2D point robot and 7-DoF Franka manipulator planning benchmarks. Our method achieves competitive planning performance at the training resolution and generalizes zero-shot across resolutions up to 16$\\times$ higher, preserving consistent planning behavior without retraining. These results demonstrate that function-space diffusion provides an effective framework for discretization-invariant motion planning.","short_abstract":"Diffusion-based motion planners have demonstrated strong performance in generating diverse and high-quality robot trajectories in cluttered environments with multiple feasible solutions. However, existing approaches typically operate on fixed-length waypoint sequences, making the learned model resolution-dependent, the...","url_abs":"https://arxiv.org/abs/2607.02977","url_pdf":"https://arxiv.org/pdf/2607.02977v1","authors":"[\"Zinuo Chang\",\"Yipu Chen\",\"Byoungwoo Park\",\"Hongzhe Yu\",\"Yongxin Chen\"]","published":"2026-07-03T05:36:07Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[\"Diffusion Model\"]","has_code":false}