The ability to design functional sequences and predict effects of variation is central to protein engineering and biotherapeutics. State-of-art computational methods rely on models that leverage evolutionary information but are inadequate for important applications where multiple sequence alignments are not robust. Such applications include the prediction of variant effects of indels, disordered proteins, and the design of proteins such as antibodies due to the highly variable complementarity determining regions. We introduce a deep generative model adapted from natural language processing for prediction and design of diverse functional sequences without the need for alignments. The model performs state-of-art prediction of missense and indel effects and we successfully design and test a diverse 105-nanobody library that shows better expression than a 1000-fold larger synthetic library. Our results demonstrate the power of the alignment-free autoregressive model in generalizing to regions of sequence space traditionally considered beyond the reach of prediction and design.