Function-Space Diffusion for Motion Planning

2026-07-03

AI Summary

This work addresses the limited generalizability of existing diffusion-based motion planning methods, which rely on fixed-length discrete trajectories and struggle to adapt across resolutions. The authors propose the first approach that models trajectories as continuous functions and formulates the diffusion process in function space. The forward process employs spectral-domain perturbations driven by Matérn-covariance Gaussian noise, while the reverse process leverages a boundary-aware Discrete Sine Transform Fourier Neural Operator (DST-FNO). This framework enables zero-shot cross-resolution generalization without retraining and strictly enforces start- and end-point constraints. Evaluated on 2D point robot navigation and 7-DoF Franka arm tasks, the method achieves strong performance at training resolution and consistently generalizes—without fine-tuning—to resolutions up to 16× higher, producing stable and coherent motion plans.

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.

Problem

• motion planning
• diffusion models
• discretization invariance
• trajectory generation
• zero-shot generalization

Innovation

• function-space diffusion
• discretization-invariant planning
• Fourier Neural Operator
• motion planning
• zero-shot generalization