We present VGM-VS, a visual servoing method built on a pretrained feed-forward visual geometry model. Given the current view and a reference image captured at the target configuration, we estimate the relative camera pose with a visual geometry model and apply it iteratively as the pose increment of a closed-loop pose-based visual servoing (PBVS) scheme. The geometry-aware representation acquired from large-scale pretraining keeps this estimate reliable when the target is occluded, weakly textured, or covers only a small part of the image. However, the scale ambiguity inherent to these models leaves the predicted translation defined up to an unknown scale, while the pose increment must be metric for robot control. We close this gap with a scene-specific metric adaptation: the robot autonomously records image--pose pairs along a predefined motion starting from the target pose, and we fine-tune the camera head on these data, jointly learning the hand--eye transform and thus removing the need for a dedicated calibration process. We evaluate our method on three real-world assembly tasks with demanding tolerances: USB-C cable picking, cable insertion, and RAM insertion. Running in real time at 30Hz, VGM-VS converges to submillimeter terminal accuracy on the cable tasks, and reaches success rates of 90--100\% when the target is moved during servoing. It converges in all trials under initial displacements of up to 30cm from the reference pose and with 50\% of the target object occluded, outperforming the compared visual servoing baselines.

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