Title: AlphaFold Distillation for Improved Inverse Protein Folding. Abstract: Inverse protein folding, i.e., designing sequences that fold into a given three-dimensional structure, is  one of the fundamental design challenges in bio-engineering and drug discovery. Traditionally, inverse folding mainly involves learning from sequences that have an experimentally resolved structure. However, the known structures cover only a tiny space of the  protein sequences, imposing limitations on the model learning. Recently proposed forward folding models, e.g., AlphaFold, offer unprecedented opportunity for accurate estimation of the structure given a protein sequence. Naturally, incorporating a forward folding model as a component of an inverse folding approach offers the potential of significantly improving the inverse folding,  as the folding model can provide a feedback on any generated sequence in the form of the predicted protein structure or a structural confidence metric. However, at present, these forward folding models are still prohibitively slow to be a part of the model optimization loop during training. In this work, we propose to perform knowledge distillation on the folding model's confidence metrics, e.g., pTM or pLDDT scores, to obtain a smaller, faster and end-to-end differentiable distilled model, which then can be included as part of the structure consistency regularized inverse folding model training. Moreover, our regularization technique is general enough and can be applied in other  design tasks, e.g., sequence-based protein infilling. Extensive experiments show a clear benefit of our method over the non-regularized baselines. E.g., in inverse folding design problems we observe up to 3% improvement in sequence recovery and up to 45% improvement in protein diversity, while still preserving structural consistency of the generated sequences.