  A popular approach to protein design is to combine a generative model with a
discriminative model for conditional sampling. The generative model samples
plausible sequences while the discriminative model guides a search for
sequences with high fitness. Given its broad success in conditional sampling,
classifier-guided diffusion modeling is a promising foundation for protein
design, leading many to develop guided diffusion models for structure with
inverse folding to recover sequences. In this work, we propose diffusioN
Optimized Sampling (NOS), a guidance method for discrete diffusion models that
follows gradients in the hidden states of the denoising network. NOS makes it
possible to perform design directly in sequence space, circumventing
significant limitations of structure-based methods, including scarce data and
challenging inverse design. Moreover, we use NOS to generalize LaMBO, a
Bayesian optimization procedure for sequence design that facilitates multiple
objectives and edit-based constraints. The resulting method, LaMBO-2, enables
discrete diffusions and stronger performance with limited edits through a novel
application of saliency maps. We apply LaMBO-2 to a real-world protein design
task, optimizing antibodies for higher expression yield and binding affinity to
several therapeutic targets under locality and developability constraints,
attaining a 99% expression rate and 40% binding rate in exploratory in vitro
experiments.
