Synthesizing controllable 6-DOF object manipulation trajectories in 3D environments is essential for enabling robots to interact with complex scenes, yet remains challenging due to the need for accurate spatial reasoning, physical feasibility, and multimodal scene understanding. Existing approaches often rely on 2D or partial 3D representations, limiting their ability to capture full scene geometry and constraining trajectory precision. We present GMT, a multimodal transformer framework that generates realistic and goal-directed object trajectories by jointly leveraging 3D bounding box geometry, point cloud context, semantic object categories, and target end poses. The model represents trajectories as continuous 6-DOF pose sequences and employs a tailored conditioning strategy that fuses geometric, semantic, contextual, and goal-oriented information. Extensive experiments on synthetic and real-world benchmarks demonstrate that GMT outperforms state-of-the-art human motion and human-object interaction baselines, such as CHOIS and GIMO, achieving substantial gains in spatial accuracy and orientation control. Our method establishes a new benchmark for learning-based manipulation planning and shows strong generalization to diverse objects and cluttered 3D environments.

Probabilistic human motion prediction aims to forecast multiple possible future movements from past observations. While current approaches report high diversity and realism, they often generate motions with undetected limb stretching and jitter. To address this, we introduce SkeletonDiffusion, a latent diffusion model that embeds an explicit inductive bias on the human body within its architecture and training. We present a new nonisotropic Gaussian diffusion formulation that aligns with the natural kinematic structure of the human skeleton and models relationships between body parts. Results show that our approach outperforms isotropic alternatives, consistently generating realistic predictions while avoiding artifacts such as limb distortion. Additionally, we identify a limitation in commonly used diversity metrics, which may favor models that produce inconsistent limb lengths within the same sequence. SkeletonDiffusion sets a new benchmark on three real-world datasets, outperforming various baselines across multiple evaluation metrics. We release the code on our project page.