Text-conditioned human-object interaction (HOI) generation requires body motion, object trajectories & rotations, and hand articulation to remain coordinated. These components differ in scale and dynamics, but must agree on contact, relative pose, and timing. A shared representation may limit the distinct structure of each stream, while independent generation prevents each stream from responding to changes in the others. Latent supervision alone also does not directly constrain contact after decoding. We propose TRACE, a continuous latent framework that keeps stream states separate and couples their updates. TRACE encodes body, object, and hand motion into separate latents and predicts each stream velocity from the complete current interaction state. Geometric losses on decoded motion further constrain contact and object-relative motion over time. The same model supports completion of any single absent stream from the other two. Frozen flow features also serve as input to a language model for HOI understanding. Experiments on InterAct, OMOMO, and BEHAVE show that joint completion training improves generation and that frozen flow features improve understanding over raw-motion encoding. On InterAct, TRACE achieves the highest contact precision, recall, and F1 among the compared methods.

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