Fig. 1: Application of a Bayesian Flow Network (BFN) to protein-sequence modelling.

BFN's update parameters of data distribution, θ, using Bayesian inference given a noised observation, y of a data sample. When applied to protein-sequence modelling, the distribution over the data is given by separate categorical distributions over the possible tokens (all amino acids and special tokens such as  < pad > ,  < bos > , and  < eos > ) at each sequence index. During training, Alice knows a ground-truth data point x, and so θ can be directly updated using noised observation of x. Bob trains a neural network to predict the sender distribution from which Alice is sampling these observations at each step (i.e., to predict the noised ground truth). During inference, when Alice is not present, Bob replaces noised observations of the ground truth with samples from the receiver distribution predicted by the network.