Multi-condition single-cell data reveals expression differences between corresponding cell subpopulations in different conditions. Here, we propose to use regression on latent spaces to simultaneously account for variance from known and latent factors. Our approach is built around multivariate regression on Grassmann manifolds. We use the method to analyze a drug treatment experiment on brain tumor biopsies. The method is a versatile new approach for identifying differentially expressed genes from single-cell data of heterogeneous cell subpopulations under arbitrary experimental designs without clustering.