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, discretised 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 modelling. The loss function directly optimises data compression and places no restrictions on the network architecture. In our experiments BFNs achieve competitive log-likelihoods for image modelling on dynamically binarized MNIST and CIFAR-10, and outperform all known discrete diffusion models on the text8 character-level language modelling task.

翻译：本文提出贝叶斯流网络（BFNs），这是一类新型生成模型，其中通过贝叶斯推断在含噪数据样本条件下对一组独立分布的参数进行修正，随后将其输入神经网络，输出第二组相互依赖的分布。从简单先验出发并迭代更新这两组分布，可生成与扩散模型逆过程相似的生成流程；但其概念更为简洁，无需前向过程。针对连续数据、离散化数据及离散数据，本文推导了离散时间与连续时间损失函数，并给出了样本生成流程。值得关注的是，离散数据的网络输入位于概率单纯形上，因此具有天然可微性，这为基于梯度的样本引导及离散领域（如语言建模）中的少步生成奠定了基础。该损失函数直接优化数据压缩，且对网络架构无任何限制。在实验中，BFNs在动态二值化MNIST和CIFAR-10图像建模任务上取得了具有竞争力的对数似然值，并在text8字符级语言建模任务中超越了所有已知离散扩散模型。