Spatial transcriptomics (ST) reveals spatial heterogeneity of gene expression, yet its resolution is limited by current platforms. Recent methods enhance resolution via H&E-stained histology, but three major challenges persist: (1) isolating expression-relevant features from visually complex H&E images; (2) achieving spatially precise multimodal alignment in diffusion-based frameworks; and (3) modeling gene-specific variation across expression channels. We propose HaDM-ST (Histology-assisted Differential Modeling for ST Generation), a high-resolution (HR) ST generation framework conditioned on H&E images and low-resolution (LR) ST. HaDM-ST includes: (i) a semantic distillation network to extract predictive cues from H&E; (ii) a spatial alignment module enforcing pixel-wise correspondence with low-res ST; and (iii) a channel-aware adversarial learner for fine-grained gene-level modeling. Experiments on 200 genes across diverse tissues and species show HaDM-ST consistently outperforms prior methods, enhancing spatial fidelity and gene-level coherence in HR ST predictions.