Robust cellular function emerges from inherently stochastic components. Understanding this apparent paradox requires innovations in connecting mechanistic models of molecular-scale randomness with statistical approaches capable of extracting structure from large-scale, heterogeneous datasets. This talk presents a framework for inferring subcellular gene expression dynamics from static spatial snapshots of mRNA molecules obtained from single-molecule imaging. By linking spatial point processes with tractable solutions to stochastic PDEs, we recover dynamic parameters efficiently and without large-scale simulation. I’ll highlight recent theoretical results, including how cell-to-cell heterogeneity improves inference, and discuss extensions to transcriptional bursting, feedback, and cell-cycle effects. The work illustrates how combining mechanistic modeling with modern machine learning can propel new insights into complex biological systems.