A central question in robot learning is how to acquire skills from the kinds of data that humans learn from: passive observation, embodied practice, and the experience of failure. Human videos provide the first of these in abundance, and prior work has shown they can initialize useful policies. Far less clear is whether they can support the second and third: whether priors extracted from human videos can ground a robot's own attempts well enough to evaluate them, correct them, and improve from them. In this work, we show that human videos can be used to learn embodiment-agnostic action, dynamics, and value representations that transfer across robot embodiments, providing the predictive foundation required for robots to autonomously improve from their own rollouts and failures. We introduce Dynamics-Guided Action Correction (DGAC), a training-free approach that leverages these adapted models to repair failed states: each failure becomes a query for which the learned models propose and rank corrective actions, turning failures into supervision for the next policy update. Across seven real-world manipulation tasks spanning both a mobile manipulator and a static manipulator arm, our approach improves success rates from 40% to 81% across multiple policy backbones, demonstrating cross-embodiment robot self-improvement from human-video priors. These results show that human priors and robot failures can be combined to enable scalable autonomous policy improvement. Project page: https://ethz-mrl.github.io/robot-self-improvement-website/.

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