Multi-arm manipulation demands precise spatiotemporal coordination, yet many centralized approaches scale poorly as team size increases. To address this, we propose CLS-DP, a decentralized multi-agent framework that enables implicit coordination under partial observability without shared global views, explicit state information, or inter-agent communication. Under the centralized training and decentralized execution (CTDE) paradigm, CLS-DP distills privileged multi-agent dynamics into a latent space. At deployment, each agent infers a collaborative latent from its local RGB observation and a shared task instruction; it then conditions the diffusion denoising process on this latent. This design enables implicit coordination with a per-agent cost independent of team size. Across six RoboFactory benchmark tasks spanning two to four agents, CLS-DP achieves a 38% mean success rate, outperforming the best centralized baseline (20%) and a decentralized ablation without the collaborative latent (9%). It also maintains superior parameter efficiency across all agent configurations. Attribution maps show that an agent conditioned on the collaborative latent places high attribution on the joints and grippers of both itself and its teammates throughout execution. This suggests that the learned latent efficiently encodes collaborative dynamics from local observation, which facilitates implicit coordination in realistic settings characterized by partial observability.

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