mlsanityData to 14 Oct 2026

Functional Mean Flow in Hilbert Space

arXiv 2511.12898 ↗First posted 17 Nov 2025cs.LG cs.CVcited by 5

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

Abstract (arXiv)

We present Functional Mean Flow (FMF) as a one-step generative model defined in infinite-dimensional Hilbert space. FMF extends the one-step Mean Flow framework to functional domains by providing a theoretical formulation for Functional Flow Matching and a practical implementation for efficient training and sampling. We also introduce an x1-prediction variant that improves stability over the original u-prediction form. The resulting framework is a practical one-step Flow Matching method applicable to a wide range of functional data generation tasks such as time series, images, PDEs, and 3D geometry.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 47 of its 58 references that are in the map. First posted on arXiv 17 Nov 2025.

Builds on

47 of 58 references.

Closest ancestors · 5

Same direction, newest first

  1. 2024Consistency Flow Matching: Defining Straight Flows with Velocity Consistency2 Jul
  2. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency models11 Jun
  3. 2023Functional Flow Matching26 May
  4. 2022Flow Matching for Generative Modeling6 Oct
  5. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 42

  1. 2017Attention Is All You Needcited by 60,361
  2. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
  3. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  4. 2020Denoising Diffusion Implicit Modelscited by 9,781
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  6. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  8. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,988
  9. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,897
  10. 2023Consistency Modelscited by 1,822
  11. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,355
  12. 2021Perceiver: General Perception with Iterative Attentioncited by 1,104
30 more
  1. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,098
  2. 2023One-step Diffusion with Distribution Matching Distillationcited by 1,019
  3. 2023Adversarial Diffusion Distillationcited by 759
  4. 2022On Distillation of Guided Diffusion Modelscited by 725
  5. 2025Mean Flows for One-step Generative Modelingcited by 561
  6. 20233DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Modelscited by 458
  7. 2021Diffusion Autoencoders: Toward a Meaningful and Decodable Representationcited by 449
  8. 2023Improved Techniques for Training Consistency Modelscited by 439
  9. 2024One Step Diffusion via Shortcut Modelscited by 391
  10. 2024Simplifying, Stabilizing and Scaling Continuous-Time Consistency Modelscited by 283
  11. 2023Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Modelscited by 236
  12. 2024Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generationcited by 214
  13. 2022The Role of ImageNet Classes in Fr'echet Inception Distancecited by 213
  14. 2022From data to functa: Your data point is a function and you can treat it like onecited by 187
  15. 2024Consistency Models Made Easycited by 144
  16. 2025Inductive Moment Matchingcited by 113
  17. 20223DILG: Irregular Latent Grids for 3D Generative Modelingcited by 93
  18. 2021Generative Models as Distributions of Functionscited by 89
  19. 2023Score-based Diffusion Models in Function Spacecited by 82
  20. 2023One-Step Diffusion Distillation via Deep Equilibrium Modelscited by 61
  21. 2022Generative Adversarial Neural Operatorscited by 52
  22. 2022Diffusion Generative Models in Infinite Dimensionscited by 49
  23. 2021Learning Signal-Agnostic Manifolds of Neural Fieldscited by 45
  24. 2023Continuous-Time Functional Diffusion Processescited by 39
  25. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generationcited by 37
  26. 2023Diffusion Probabilistic Fieldscited by 28
  27. 2023∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified Statescited by 21
  28. 2023Functional Diffusioncited by 13
  29. 2024∞-Brush: Controllable Large Image Synthesis with Diffusion Models in Infinite Dimensionscited by 8
  30. 2022Energy-Based Models for Functional Data using Path Measure Tiltingcited by 5

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026Trajectory Consistency for One-Step Generation on Euler Mean Flowscited by 2
  2. 2026Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Spacecited by 1
  3. 2026Discretization and Statistical Consistency of Functional Flow Matchingcited by 1
  4. 2026A Few-Step Generative Model on Cumulative Flow Mapscited by 0
  5. 2026SNaP: One-Step Posterior Sampling for Noisy Inverse Problemscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Flow Straight and Fast in Hilbert Space: Functional Rectified Flow
  2. 2026Improving Function Space Flow Matching with Kernel Optimal Transport
  3. 2024Convergence Analysis of Flow Matching in Latent Space with Transformers
  4. 2026A Flow Matching Algorithm for Many-Shot Adaptation to Unseen Distributions
  5. 2025Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans
  6. 2026Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Support
  7. 2024Local Flow Matching Generative Models
  8. 2024Explicit Flow Matching: On The Theory of Flow Matching Algorithms with Applications