“Bayesian Flow Networks”, Alex Graves, Rupesh Kumar Srivastava, Timothy Atkinson, Faustino Gomez2023-08-14 (discrete diffusion model, compression, Bayes)⁠:

This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input to a neural network that outputs a second, interdependent distribution.

Starting from a simple prior and iteratively updating the two distributions yields a generative procedure similar to the reverse process of diffusion models; however it is conceptually simpler in that no forward process is required. Discrete and continuous-time loss functions are derived for continuous, discretized and discrete data, along with sample generation procedures.

Notably, the network inputs for discrete data lie on the probability simplex, and are therefore natively differentiable, paving the way for gradient-based sample guidance and few-step generation in discrete domains such as language modeling. The loss function directly optimizes data compression and places no restrictions on the network architecture.

In our experiments BFNs achieve competitive log-likelihoods for image modeling on dynamically binarized MNIST and CIFAR-10, and outperform all known discrete diffusion models on the text8 character-level language modeling task.