We resolve difficulties in training and sampling from a discrete generative model by learning a smoothed energy function, sampling from the smoothed data manifold with Langevin Markov chain Monte Carlo (MCMC), and projecting back to the true data manifold with one-step denoising. Our $\textit{Discrete Walk-Jump Sampling}$ formalism combines the contrastive divergence training of an energy-based model and improved sample quality of a score-based model, while simplifying training and sampling by requiring only a single noise level. We evaluate the robustness of our approach on generative modeling of antibody proteins and introduce the $\textit{distributional conformity score}$ to benchmark protein generative models. By optimizing and sampling from our models for the proposed distributional conformity score, 97-100\% of generated samples are successfully expressed and purified and 70\% of functional designs show equal or improved binding affinity compared to known functional antibodies on the first attempt in a single round of laboratory experiments. We also report the first demonstration of long-run fast-mixing MCMC chains where diverse antibody protein classes are visited in a single MCMC chain.

We introduce AbDiffuser, an equivariant and physics-informed diffusion model for the joint generation of antibody 3D structures and sequences. AbDiffuser is built on top of a new representation of protein structure, relies on a novel architecture for aligned proteins, and utilizes strong diffusion priors to improve the denoising process. Our approach improves protein diffusion by taking advantage of domain knowledge and physics-based constraints; handles sequence-length changes; and reduces memory complexity by an order of magnitude, enabling backbone and side chain generation. We validate AbDiffuser in silico and in vitro. Numerical experiments showcase the ability of AbDiffuser to generate antibodies that closely track the sequence and structural properties of a reference set. Laboratory experiments confirm that all 16 HER2 antibodies discovered were expressed at high levels and that 57.1% of the selected designs were tight binders.