Spatial transcriptomics (ST) links gene expression with tissue morphology but remains expensive and low-throughput, motivating surrogates that infer expression from routine histology. Whole-slide H&E-to-ST inference pairs a gigapixel image with gene measurements at a sparse, irregular set of locations, making multiscale modeling challenging without incurring dense-grid overhead or quadratic token mixing. We propose HiST, a hierarchical sparse transformer that treats measured locations as a lattice-indexed sparse field and builds a dyadic encoder--decoder directly on the active tissue footprint. HiST combines sparse window attention for local geometric correspondence with resolution-changing operators for rapid multiscale context integration. For a fixed window size, the dominant runtime and memory scale with the number of observed locations rather than the dense slide area. To mitigate slide-specific acquisition variation, HiST adds a bottlenecked global conditioning pathway via a \emph{slide calibration token} that summarizes slide-level context and conditions local representations. On a multi-organ benchmark spanning diverse tissues and acquisition sources, HiST improves predictive performance over recent baselines while reducing runtime and peak memory.