Due to its internal state or external environment, a cell’s gene expression profile contains multiple signatures, simultaneously encoding information about its characteristics. Disentangling these factors of variations from single-cell data is needed to recover multiple layers of biological information and extract insight into the individual and collective behavior of cellular populations. While several recent methods were suggested for biological disentanglement, each has its limitations; they are either task-specific, cannot capture inherent nonlinear or interaction effects, cannot integrate layers of experimental data, or do not provide a general reconstruction procedure. We presentbiolord, a deep generative framework for disentangling known and unknown attributes in single-cell data. Biolord exposes the distinct effects of different biological processes or tissue structure on cellular gene expression. Based on that, biolord allows generating experimentally-inaccessible cell states by virtually shifting cells across time, space, and biological states. Specifically, we showcase accurate predictions of cellular responses to drug perturbations and generalization to predict responses to unseen drugs. Further, biolord disentangles spatial, temporal, and infection-related attributes and their associated gene expression signatures in a single-cell atlas ofPlasmodiuminfection progression in the mouse liver. Biolord can handle partially labeled attributes by predicting a classification for missing labels, and hence can be used to computationally extend an infected hepatocyte population identified at a late stage of the infection to earlier stages. Biolord applies to diverse biological settings, is implemented using the scvi-tools library, and is released as open-source software athttps://github.com/nitzanlab/biolord.