Language Models (LMs) encode substantial knowledge in their parameters, yet it remains unclear how to transfer such knowledge in a fine-grained manner, namely parametric knowledge transfer (PKT). A central challenge is to make cross-scale transfer effective and efficient when source and target models differ in architecture and parameterization, making direct parameter reuse strongly limited by neural incompatibility. In this paper, we identify latent semantic alignment as the key prerequisite for cross-scale knowledge transfer. Instead of directly moving layer parameters, our approach uses activations as the transfer medium. \textsc{SemAlign} has two stages: an \emph{layer attribution} stage that attributes task-relevant source layers and selects exactly one source layer for each target layer, and a \emph{semantic alignment} stage that pairs them layer by layer and optimizes the target with source-side semantic supervision. The alignment is carried out in latent space through semantic decomposition and recomposition. During the shallow-to-deep transfer, only the frontier target layer is trainable. The layer objective supervises the residual contribution of that layer by matching centered token-token relation geometry against an aligned supervisory residual, while output KL preserves source-level predictive behavior. The transferred medium is therefore neither a parameter block nor an absolute hidden state, but target-space residual geometry induced by paired source-layer supervision. Evaluations on four benchmarks demonstrate the efficacy of \textsc{SemAlign}, and further analysis confirms that semantic decomposition and recomposition provide a stable mechanism for cross-scale knowledge transfer.