Posterior Mean Matching: Generative Modeling through Online Bayesian Inference
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 19 of its 34 references that are in the map. First posted on arXiv 17 Dec 2024.
Builds on
19 of 34 references.
Closest ancestors · 8
Same direction, newest first
- 2024Treeffuser: Probabilistic Predictions via Conditional Diffusions with Gradient-Boosted Trees11 Jun
- 2023Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces18 May
- 2022Scalable Diffusion Models with Transformers19 Dec
- 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
- 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
- 2021Diffusion Models Beat GANs on Image Synthesis11 May
- 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
- 2020Denoising Diffusion Probabilistic Models19 Jun
Other references · 11
- 2017Attention Is All You Needcited by 59,932
- 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
- 2015Variational Inference with Normalizing Flowscited by 2,161
- 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
- 2014NICE: Non-linear Independent Components Estimationcited by 1,052
- 2016Conditional Image Generation with PixelCNN Decoderscited by 859
- 2024Simple and Effective Masked Diffusion Language Modelscited by 800
- 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 712
- 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 606
- 2023Bayesian Flow Networkscited by 62
- 2023Learning to Jump: Thinning and Thickening Latent Counts for Generative Modelingcited by 15
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Citing papers per year: 2025: 1; 2026: 1.
2 papers.
Similar, not cited
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- 2026Reducing Memorisation in Generative Models via Riemannian Bayesian Inference
- 2022From Denoising Diffusions to Denoising Markov Models
- 2026Semi-Supervised Generative Learning via Latent Space Distribution Matching
- 2024Generator Matching: Generative modeling with arbitrary Markov processes
- 2025Generative diffusion posterior sampling for informative likelihoods
- 2026Proximal-Based Generative Modeling for Bayesian Inverse Problems