Latent Action Models (LAMs) can capture manipulation priors from action-free videos, but discrete latents usually impose a granularity bottleneck, limiting their ability to represent fine-grained action. Recent continuous alternatives mitigate this, but they are typically used as proxies for world modeling and require a further planning step to produce executable actions. We thus introduce UniLAP, a unified continuous latent-action policy that models the latent space via flow matching and bypasses reliance on future frames during inference. By distilling a LAM teacher with a flow-adaptive objective, UniLAP inherits the teacher's action representation while retaining the multimodal distribution of feasible behaviors. To decouple latent representations from task-irrelevant appearance, we extract a label-free motion target to isolate relevant kinematic cues from spurious visual dynamics. With the established embodiment-agnostic latent manifold, UniLAP can be easily adapted to novel platforms. Pretrained on multi-source videos at a compact 1.1B parameter scale, UniLAP outperforms state-of-the-art latent-action and Vision-Language-Action (VLA) baselines across hand pose forecasting, single-arm and humanoid manipulation, and real-world deployment.

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