mlsanityData to 14 Oct 2026

Posterior Flow Matching

arXiv 2610.13994 ↗First posted 26 Sep 2026cs.LG cs.AI cs.CVcited by 0

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Flow matching learns how to transport noise toward data, but its mean prediction does not directly report the endpoint uncertainty remaining at an intermediate state. This paper introduces Posterior Flow Matching (PFM), a general generative modeling framework that learns conditional velocity means and componentwise variances with a Gaussian posterior model. The same model evaluation supplies both a transport prediction and endpoint uncertainty, making posterior diagnostics available throughout generation. These learned moments support a mean-driven ordinary differential equation (ODE) and a posterior-driven stochastic differential equation (SDE), whose local noise scales adapt to the predicted uncertainty. Across image, point-cloud, molecular, and action generation, PFM improves generation quality and provides endpoint-posterior readouts throughout generation.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 57 of its 71 references that are in the map. First posted on arXiv 26 Sep 2026.

Builds on

57 of 71 references.

Closest ancestors · 18

Same direction, newest first

  1. 2026Drift Flow Matching17 May
  2. 2026Uncertainty in a Single Pass: A Closed-Form Identity for One-Step Flow Matching1 May
  3. 2026Posterior Augmented Flow Matching1 May
  4. 2026Transition Flow Matching16 Mar
  5. 2026Flow Matching with Uncertainty Quantification and Guidance10 Feb
  6. 2025Learning Straight Flows: Variational Flow Matching for Efficient Generation15 Nov
  7. 2025Hierarchical Rectified Flow Matching with Mini-Batch Couplings17 Jul
  8. 2025Towards Hierarchical Rectified Flow24 Feb
  9. 2025Variational Rectified Flow Matching13 Feb
  10. 2024Flow Matching Guide and Code9 Dec
  11. 2024Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow9 Oct
  12. 2024Improving the Training of Rectified Flows30 May
6 more
  1. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Step19 Mar
  2. 2023Equivariant flow matching26 Jun
  3. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplings28 Apr
  4. 2023Improving and generalizing flow-based generative models with minibatch optimal transport1 Feb
  5. 2022Flow Matching for Generative Modeling6 Oct
  6. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 39

  1. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 30,186
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  5. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,498
  6. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,248
  7. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,181
  8. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  9. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  10. 2016Improved Techniques for Training GANscited by 2,970
  11. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,897
  12. 2023Diffusion Policy: Visuomotor Policy Learning via Action Diffusioncited by 2,838
27 more
  1. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  2. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  3. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 737
  4. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 735
  5. 2019On Variational Bounds of Mutual Informationcited by 559
  6. 2019PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flowscited by 488
  7. 2021Implicit Behavioral Cloningcited by 452
  8. 2023Simple diffusion: End-to-end diffusion for high resolution imagescited by 422
  9. 2024Pyramidal Flow Matching for Efficient Video Generative Modelingcited by 366
  10. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Modelscited by 334
  11. 2025Diffusion Transformers with Representation Autoencoderscited by 295
  12. 2020GEOM: Energy-annotated molecular conformations for property prediction and molecular generationcited by 243
  13. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 182
  14. 2015Variational Information Maximisation for Intrinsically Motivated Reinforcement Learningcited by 144
  15. 2023Stochastic interpolants with data-dependent couplingscited by 100
  16. 2025The Principles of Diffusion Modelscited by 76
  17. 2024Diffusion Self-Distillation for Zero-Shot Customized Image Generationcited by 47
  18. 2024ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generationcited by 43
  19. 2023BayesDiff: Estimating Pixel-wise Uncertainty in Diffusion via Bayesian Inferencecited by 35
  20. 2023On the Posterior Distribution in Denoising: Application to Uncertainty Quantificationcited by 33
  21. 2025Generative Uncertainty in Diffusion Modelscited by 23
  22. 2024Diffusion Model Guided Sampling with Pixel-Wise Aleatoric Uncertainty Estimationcited by 20
  23. 2026Not All Directions Matter: Towards Structured and Task-Aware Low-Rank Model Adaptationcited by 14
  24. 2025CAD-VAE: Leveraging Correlation-Aware Latents for Comprehensive Fair Disentanglementcited by 11
  25. 2025Beyond Editing Pairs: Fine-Grained Instructional Image Editing via Multi-Scale Learnable Regionscited by 7
  26. 2025Stochastic Interpolants via Conditional Dependent Couplingcited by 7
  27. 2026Flowing with Confidencecited by 1

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  1. 2024Flow Matching Posterior Sampling: A Training-free Conditional Generation for Flow Matching
  2. 2025Conditional Flow Matching for Bayesian Posterior Inference
  3. 2025LeDiFlow: Learned Distribution-guided Flow Matching to Accelerate Image Generation
  4. 2026Coreset-Induced Conditional Velocity Flow Matching
  5. 2026Flow Matching is Adaptive to Manifold Structures
  6. 2026Random Process Flow Matching: Generative Implicit Representations of Multivariate Random Fields
  7. 2026Noise-Robust Conditional Flow Matching: Generating Clean Samples from Noisy Datasets
  8. 2026Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Support