Accurate cell marker identification in single-cell RNA-seq data is crucial for understanding cellular diversity and function. An ideal marker is highly specific in identifying cells that are similar in terms of function and state. Current marker identification methods, commonly based on clustering and differential expression, capture general cell-type markers but often miss markers for subtypes or functional cell subsets, with their performance largely dependent on clustering quality. Moreover, cluster-independent approaches tend to favor genes that lack the specificity required to characterize regions within the transcriptomic space at multiple scales. Here we introduce Localized Marker Detector (LMD), a novel tool to identify "localized genes" - genes with expression profiles specific to certain groups of highly similar cells - thereby characterizing cellular diversity in a multi-resolution and fine-grained manner. LMD's strategy involves building a cell-cell affinity graph, diffusing the gene expression value across the cell graph, and assigning a score to each gene based on its diffusion dynamics. We show that LMD exhibits superior accuracy in recovering known cell-type markers in the Tabula Muris bone marrow dataset relative to other methods for marker identification. Notably, markers favored by LMD exhibit localized expression, whereas markers prioritized by other clustering-free algorithms are often dispersed in the transcriptomic space. We further group the markers suggested by LMD into functional gene modules to improve the separation of cell types and subtypes in a more fine-grained manner. These modules also identify other sources of variation, such as cell cycle status. In conclusion, LMD is a novel algorithm that can identify fine-grained markers for cell subtypes or functional states without relying on clustering or differential expression analysis. LMD exploits the complex interactions among cells and reveals cellular diversity at high resolution.