Title: Fold2Seq: A Joint Sequence(1D)-Fold(3D) Embedding-based Generative Model for Protein Design. Abstract: Designing novel protein sequences consistent with a desired 3D structure  or fold, often referred to as the inverse protein folding problem, is a central, but non-trivial, task in protein engineering.  It has a wide range of applications  in energy, biomedicine, and materials science. However, challenges exist due to the complex sequence-fold relationship and difficulties associated with  modeling 3D folds. To overcome these challenges, we propose Fold2Seq, a novel transformer-based generative framework for designing protein sequences conditioned on a specific fold. Our model learns a fold  embedding from the density of the secondary structural elements in 3D voxels, and then models  the complex sequence-structure relationship by learning a joint sequence-fold embedding. Experiments on  high-resolution, complete, and single-structure test set demonstrate improved  performance of Fold2Seq in terms of speed and reliability for sequence design, compared to existing baselines including the state-of-the-art RosettaDesign and other neural net-based approaches. The unique advantages of fold-based Fold2Seq becomes more evident on diverse real-world test sets comprised of low-resolution, incomplete, or ensemble structures,  in comparison to a structure-based model. 