mlsanityData to 7 Oct 2026

Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equations

arXiv 2404.15766 ↗First posted 24 Apr 2024cs.LG cs.AIcited by 28

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Bayesian flow networks (BFNs) iteratively refine the parameters, instead of the samples in diffusion models (DMs), of distributions at various noise levels through Bayesian inference. Owing to its differentiable nature, BFNs are promising in modeling both continuous and discrete data, while simultaneously maintaining fast sampling capabilities. This paper aims to understand and enhance BFNs by connecting them with DMs through stochastic differential equations (SDEs). We identify the linear SDEs corresponding to the noise-addition processes in BFNs, demonstrate that BFN's regression losses are aligned with denoise score matching, and validate the sampler in BFN as a first-order solver for the respective reverse-time SDE. Based on these findings and existing recipes of fast sampling in DMs, we propose specialized solvers for BFNs that markedly surpass the original BFN sampler in terms of sample quality with a limited number of function evaluations (e.g., 10) on both image and text datasets. Notably, our best sampler achieves an increase in speed of 5~20 times for free. Our code is available at https://github.com/ML-GSAI/BFN-Solver.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 45 of its 58 references that are in the map. First posted on arXiv 24 Apr 2024.

Builds on

45 of 58 references.

Closest ancestors · 24

Same direction, newest first

  1. 2023Gaussian Mixture Solvers for Diffusion Models2 Nov
  2. 2023SA-Solver: Stochastic Adams Solver for Fast Sampling of Diffusion Models10 Sep
  3. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis4 Jul
  4. 2023Reflected Diffusion Models10 Apr
  5. 2023One Transformer Fits All Distributions in Multi-Modal Diffusion at Scale12 Mar
  6. 2023UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models9 Feb
  7. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models2 Nov
  8. 2022Categorical SDEs with Simplex Diffusion26 Oct
  9. 2022Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning8 Aug
  10. 2022Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matching16 Jun
  11. 2022Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models15 Jun
  12. 2022gDDIM: Generalized denoising diffusion implicit models11 Jun
12 more
  1. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  2. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  3. 2022A Continuous Time Framework for Discrete Denoising Models30 May
  4. 2022Pseudo Numerical Methods for Diffusion Models on Manifolds20 Feb
  5. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models17 Jan
  6. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  7. 2021Variational Diffusion Models1 Jul
  8. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  9. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  11. 2020Denoising Diffusion Implicit Models6 Oct
  12. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 21

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2023GPT-4 Technical Reportcited by 18,132
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  5. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  6. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,006
  7. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,765
  8. 2022Make-A-Video: Text-to-Video Generation without Text-Video Datacited by 1,725
  9. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  10. 2023ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillationcited by 1,207
  11. 2022Imagic: Text-Based Real Image Editing with Diffusion Modelscited by 1,172
  12. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
9 more
  1. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  2. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  3. 2022Text2LIVE: Text-Driven Layered Image and Video Editingcited by 312
  4. 2020Swapping Autoencoder for Deep Image Manipulationcited by 215
  5. 2021Autoregressive Diffusion Modelscited by 208
  6. 2023RAPHAEL: Text-to-Image Generation via Large Mixture of Diffusion Pathscited by 141
  7. 2023TESS: Text-to-Text Self-Conditioned Simplex Diffusioncited by 63
  8. 2023The Blessing of Randomness: SDE Beats ODE in General Diffusion-based Image Editingcited by 61
  9. 2020Efficient Learning of Generative Models via Finite-Difference Score Matchingcited by 49

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 7; 2025: 12; 2026: 9.

28 papers.

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  1. 2025Large Language Diffusion Modelscited by 872
  2. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 606
  3. 2024Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Datacited by 371
  4. 2024Scaling up Masked Diffusion Models on Textcited by 195
  5. 2025LLaDA-V: Large Language Diffusion Models with Visual Instruction Tuningcited by 145
  6. 2025Efficient Diffusion Models: A Surveycited by 35
  7. 2024Identifying and Solving Conditional Image Leakage in Image-to-Video Diffusion Modelcited by 27
  8. 2025Flow Matching Meets Biology and Life Science: A Surveycited by 14
  9. 2025Straight-Line Diffusion Model for Efficient 3D Molecular Generationcited by 8
  10. 2024Empower Structure-Based Molecule Optimization with Gradient Guided Bayesian Flow Networkscited by 6
  11. 2026Context Tokens are Anchors: Understanding the Repetition Curse in dMLLMs from an Information Flow Perspectivecited by 6
  12. 2026Membership Inference Attacks Against Fine-tuned Diffusion Language Modelscited by 5
16 more
  1. 2025Generative Modeling with Bayesian Sample Inferencecited by 4
  2. 2025Manipulating 3D Molecules in a Fixed-Dimensional E(3)-Equivariant Latent Spacecited by 3
  3. 2024ParamReL: Learning Parameter Space Representation via Progressively Encoding Bayesian Flow Networkscited by 2
  4. 2025Incomplete Data, Complete Dynamics: A Diffusion Approachcited by 2
  5. 2025Target-Guided Bayesian Flow Networks for Quantitatively Constrained CAD Generationcited by 2
  6. 2026Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspectivecited by 2
  7. 2025MolPIF: A Parameter Interpolation Flow Model for Molecule Generationcited by 1
  8. 2026Masked Diffusion Generative Recommendationcited by 1
  9. 2026A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Modelscited by 1
  10. 2026Efficient Long-Context Modeling in Diffusion Language Models via Block Approximate Sparse Attentioncited by 1
  11. 2026LLaDA MoE v2: Scaling Mixture-of-Experts Diffusion Language Modelscited by 1
  12. 2024Sampling Out-of-Distribution Chemical Spaces via Bayesian Flowcited by 0
  13. 2025IgCraft: A versatile sequence generation framework for antibody discovery and engineeringcited by 0
  14. 2025Discrete Bayesian Sample Inference for Graph Generationcited by 0
  15. 2026Observation-Aligned Mask Priors for Learning Physical Fields from Authentic Occlusionscited by 0
  16. 2026Bayesian Flow Networks for Offline Trajectory Planningcited by 0

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  6. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
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