Function-Space Diffusion for Motion Planning

• URL: http://arxiv.org/abs/2607.02977v1
• Date: Fri, 03 Jul 2026 05:36:07 GMT
• Title: Function-Space Diffusion for Motion Planning
• Abstract summary: Diffusion-based motion planners have demonstrated strong performance in generating diverse and high-quality robot trajectories.<n>We propose Function-Space Diffusion for Motion Planning (FSD-MP), a diffusion-based motion planner that performs diffusion directly in function space.<n>Our method achieves competitive planning performance at the training resolution and generalizes zero-shot across resolutions up to 16$times$ higher.
• Score: 21.931455331420725
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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