  Inverse protein folding -- the task of predicting a protein sequence from its
backbone atom coordinates -- has surfaced as an important problem in the "top
down", de novo design of proteins. Contemporary approaches have cast this
problem as a conditional generative modelling problem, where a large generative
model over protein sequences is conditioned on the backbone. While these
generative models very rapidly produce promising sequences, independent draws
from generative models may fail to produce sequences that reliably fold to the
correct backbone. Furthermore, it is challenging to adapt pure generative
approaches to other settings, e.g., when constraints exist. In this paper, we
cast the problem of improving generated inverse folds as an optimization
problem that we solve using recent advances in "deep" or "latent space"
Bayesian optimization. Our approach consistently produces protein sequences
with greatly reduced structural error to the target backbone structure as
measured by TM score and RMSD while using fewer computational resources.
Additionally, we demonstrate other advantages of an optimization-based approach
to the problem, such as the ability to handle constraints.
