用在线贝叶斯推断构建生成模型，可灵活处理图像、文本等多模态数据。
Posterior Mean Matching: Generative Modeling through Online Bayesian Inference
- 基于共轭先验的在线贝叶斯更新，逐步优化噪声数据分布
- 在图像和语言建模上达到与扩散模型相当的性能
- 支持多种数据类型，且能导出新型泊松过程驱动的SDE
本文提出后验均值匹配（PMM），一种基于贝叶斯推断的生成建模新方法。PMM利用共轭分布对建模图像、文本等多模态复杂数据，通过在线贝叶斯推断迭代优化噪声近似分布。该方法灵活，其机制建立在通用贝叶斯模型之上：我们开发了针对实值数据的正态-正态模型、计数数据的伽马-泊松模型和离散数据的狄利克雷-多项式模型。对于正态-正态PM，我们证明其连续时间形式收敛至随机微分方程（SDE）；对于伽马-泊松PM，我们推导出由考克斯过程驱动的新型SDE，突破传统布朗运动框架。实验显示，PMM在语言建模和图像生成任务中性能与现有生成模型相当。
原文摘要 · Abstract (English)
This paper introduces posterior mean matching (PMM), a new method for generative modeling that is grounded in Bayesian inference. PMM uses conjugate pairs of distributions to model complex data of various modalities like images and text, offering a flexible alternative to existing methods like diffusion models. PMM models iteratively refine noisy approximations of the target distribution using updates from online Bayesian inference. PMM is flexible because its mechanics are based on general Bayesian models. We demonstrate this flexibility by developing specialized examples: a generative PMM model of real-valued data using the Normal-Normal model, a generative PMM model of count data using a Gamma-Poisson model, and a generative PMM model of discrete data using a Dirichlet-Categorical model. For the Normal-Normal PMM model, we establish a direct connection to diffusion models by showing that its continuous-time formulation converges to a stochastic differential equation (SDE). Additionally, for the Gamma-Poisson PMM, we derive a novel SDE driven by a Cox process, which is a significant departure from traditional Brownian motion-based generative models. PMMs achieve performance that is competitive with generative models for language modeling and image generation.
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