Single-cell RNA sequencing and other profiling assays have helped interrogate cells at unprecedented resolution and scale, but are inherently destructive. Raman microscopy reports on the vibrational energy levels of proteins and metabolites in a label-free and nondestructive manner at subcellular spatial resolution, but it lacks genetic and molecular interpretability. Here we present Raman2RNA (R2R), a method to infer single-cell expression profiles in live cells through label-free hyperspectral Raman microscopy images and domain translation. We predict single-cell RNA sequencing profiles nondestructively from Raman images using either anchor-based integration with single molecule fluorescence in situ hybridization, or anchor-free generation with adversarial autoencoders. R2R outperformed inference from brightfield images (cosine similarities: R2R >0.85 and brightfield <0.15). In reprogramming of mouse fibroblasts into induced pluripotent stem cells, R2R inferred the expression profiles of various cell states. With live-cell tracking of mouse embryonic stem cell differentiation, R2R traced the early emergence of lineage divergence and differentiation trajectories, overcoming discontinuities in expression space. R2R lays a foundation for future exploration of live genomic dynamics.