AutodidactWAM: Cross-Modal Self-Distillation from Generated Video to Robot Actions

World-action models (WAMs) such as Cosmos 3 jointly generate future video and robot actions from an observation and instruction. Adapting one such model with a lightweight LoRA fine-tune to a previously unseen robot, a Unitree G1 humanoid with five-fingered BrainCo hands, exposes a video-action asymmetry: the video renders plausible task executions, while the co-generated action is systematically mis-targeted. We evaluate closed-loop real-robot trials at three cumulative stages: pre-grasp, grasp, and pick-and-place. The native action succeeds only approximately 17%, 10%, and 7% of the time, respectively, and performs worse on held-out objects. We propose AutodidactWAM, a hand-pose estimator trained without teleoperation, followed by inverse kinematics, that runs on the model's generated video to recover action estimates. Paired with the native prediction, these recovered actions provide preferred targets for fine-tuning only the action-related layers, while the generated video is teacher-forced. We compare supervised relabeling with a rectified-flow adaptation of Diffusion-DPO. After one-time embodiment adaptation, self-distillation requires no additional task-specific teleoperation. The recovered-action gate reaches approximately 75%, 47%, and 42% pre-grasp, grasp, and pick-and-place success, compared with 17%, 10%, and 7% for the native action. A hybrid objective combining preference supervision, supervised target fitting, and Cartesian trajectory anchoring (DPO+SFT+DTW) performs best: on Oreo, the training object, it reaches 90% pre-grasp and 20% full-task success; on a held-out object, it reaches 80% and 30%. Plain Flow-DPO reaches 0% success despite 1.000 validation preference accuracy, indicating that the combination of training objectives, rather than the contrastive objective alone, drives the observed gains.