mlsanityData to 7 Oct 2026

Generative Modeling with Bayesian Sample Inference

arXiv 2502.07580 ↗First posted 11 Feb 2025cs.LG stat.MLcited by 4

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Abstract (arXiv)

We present a novel view of diffusion-like generative modeling from the perspective of iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we formulate the sampling process in the language of Bayesian probability: at each step, a model predicts the unknown sample from our current belief state and we compute a posterior belief from that prediction. Based on this formulation, we propose the generative model Bayesian Sample Inference (BSI). In addition to a rigorous theoretical analysis, we show that our perspective includes Bayesian Flow Networks (BFNs) and that BSI and BFNs represent the two opposite ends of a range of isotropic hyper-priors over the initial belief state. In our experiments, we demonstrate that BSI improves sample quality over both BFNs and the closely related Variational Diffusion Models on ImageNet32 and ImageNet64, while achieving equivalent log-likelihoods on both datasets.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 37 of its 54 references that are in the map. First posted on arXiv 11 Feb 2025.

Builds on

37 of 54 references.

References · 37

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
  3. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  4. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  5. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  6. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  7. 2020Denoising Diffusion Implicit Modelscited by 9,655
  8. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  9. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  10. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  11. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  12. 2022Scalable Diffusion Models with Transformerscited by 5,931
25 more
  1. 2022Generative Adversarial Networkscited by 5,603
  2. 2022Flow Matching for Generative Modelingcited by 5,426
  3. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  4. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  5. 2015Variational Inference with Normalizing Flowscited by 2,161
  6. 2021Variational Diffusion Modelscited by 1,145
  7. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  8. 2023Improved Techniques for Training Consistency Modelscited by 430
  9. 2017A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasetscited by 374
  10. 2015A note on the evaluation of generative modelscited by 291
  11. 2022Generative Modelling With Inverse Heat Dissipationcited by 164
  12. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecastingcited by 86
  13. 2023Bayesian Flow Networkscited by 62
  14. 2024Sequential Controlled Langevin Diffusionscited by 47
  15. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 46
  16. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecastingcited by 40
  17. 2019HiLLoC: Lossless Image Compression with Hierarchical Latent Variable Modelscited by 36
  18. 2024Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equationscited by 28
  19. 2023Add and Thin: Diffusion for Temporal Point Processescited by 22
  20. 2023Fast Sampling via Discrete Non-Markov Diffusion Models with Predetermined Transition Timecited by 20
  21. 2024Unlocking Point Processes through Point Set Diffusioncited by 12
  22. 2025Unified Guidance for Geometry-Conditioned Molecular Generationcited by 7
  23. 2023Assessing Robustness via Score-Based Adversarial Image Generationcited by 6
  24. 2024Unfolding Time: Generative Modeling for Turbulent Flows in 4Dcited by 4
  25. 2024Posterior Mean Matching: Generative Modeling through Online Bayesian Inferencecited by 2

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Cited by year

Citing papers per year: 2025: 4.

4 papers.

  1. 2025Edit-Based Flow Matching for Temporal Point Processescited by 7
  2. 2025Flow Matching Neural Processescited by 6
  3. 2025Information Theoretic Learning for Diffusion Models with Warm Startcited by 3
  4. 2025Discrete Bayesian Sample Inference for Graph Generationcited by 0

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  1. 2025Generative Uncertainty in Diffusion Models
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  3. 2024Posterior sampling via Langevin dynamics based on generative priors
  4. 2025Diffusion Models: A Mathematical Introduction
  5. 2023A Complete Recipe for Diffusion Generative Models
  6. 2025Information-Theoretic Proofs for Diffusion Sampling
  7. 2025Generative diffusion posterior sampling for informative likelihoods
  8. 2025Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey