To learn effectively, animals must generalize across related contexts yet distinguish between them. Generalization relies on low-dimensional neural manifolds throughout the neocortex1,2, which accelerate learning by constraining neural activity to task-relevant axes3.Conversely, context separation is thought to depend on neural expansion layers that can project information into high-dimensional feature spaces4,5, most famously cerebellar granule cells (GrCs)6-8. Here, to investigate the generalization-separation trade-off, we simultaneously imaged key nodes in the universal cortico-cerebellar pathway9-premotor layer 5 pyramidal tract (L5PT) and GrCs-in mice during parallel learning of two distinct skills with a shared temporal structure. Rather than expanding the cortical representations, GrCs retained their low-rank encoding of each task. Across contexts, despite stable cortico-cerebellar coupling, L5PT activity patterns generalized, whereas GrC patterns temporally remapped. But rather than independently scrambling, GrC populations remapped coherently: their low-dimensional trajectories 'rotated' apart between tasks, separating the contexts while preserving the cortical geometry of each. Moreover, GrC trajectories diverged most strongly in expert mice. This suggests a fundamental architectural division of labour: the cortex provides invariant dynamic primitives for smooth generalization, whereas cerebellar activity reconfigures them to drive context-specific output.