用任务相关的噪声模型提升机器人运动规划的效率和顺滑度。

We propose a novel hierarchical 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 generalize the standard diffusion process to biased, non-isotropic corruption with closed-form forward and posterior expressions. Building on this formulation, our hierarchical design separates prior instantiation from trajectory denoising. At the upper level, the model predicts sparse, task-centric key states and their associated timings, which instantiate a structured Gaussian prior (mean and covariance). At the lower level, the full trajectory is denoised under this fixed prior, treating the upper-level outputs as noisy observations. Experiments on Maze2D goal-reaching and KUKA block stacking show consistently higher success rates and smoother trajectories than isotropic baselines, achieving dataset-level smoothness substantially earlier during training. Ablation studies further show that explicitly structuring the corruption process provides benefits beyond neural conditioning the denoising network alone. Overall, our approach concentrates the prior's probability mass near feasible and semantically meaningful trajectories. Our project page is available at https://hta-diffusion.github.io.