Structured-Diffuser: Diffusion with Task-Conditioned Structured Priors for Motion Planning

We propose Structured-Diffuser, a diffusion planner that embeds task and motion structure directly into the noise model. Unlike standard diffusion-based planners that rely on zero-mean, isotropic Gaussian corruption, we introduce task-conditioned structured Gaussians whose means and covariances are derived from Gaussian Process Motion Planning (GPMP), explicitly encoding trajectory smoothness and task semantics in the prior. We first formulate diffusion under a task-conditioned, non-isotropic Gaussian prior with closed-form forward and posterior expressions. Building on this formulation, our hierarchical design separates prior instantiation from trajectory denoising. At the upper level, sparse task-centric key states and timings are obtained, which instantiate a structured Gaussian prior (mean and covariance). At the lower level, the full trajectory is denoised under this prior, treating the upper-level outputs as noisy observations. Experiments across three motion-planning tasks show improved task success and training efficiency, with additional gains in data efficiency, trajectory smoothness, and position--velocity consistency where evaluated. Ablation studies further show that explicitly structuring the corruption process provides benefits beyond neurally conditioning the denoising network alone. Overall, our approach concentrates the prior's probability mass around task-relevant, temporally structured trajectories. We additionally demonstrate deployment on a physical G1 humanoid.