mlsanityData to 14 Oct 2026

Probability-Flow ODE in Infinite-Dimensional Function Spaces

arXiv 2503.10219 ↗First posted 13 Mar 2025cs.LG stat.MLcited by 5

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Recent advances in infinite-dimensional diffusion models have demonstrated their effectiveness and scalability in function generation tasks where the underlying structure is inherently infinite-dimensional. To accelerate inference in such models, we derive, for the first time, an analog of the probability-flow ODE (PF-ODE) in infinite-dimensional function spaces. Leveraging this newly formulated PF-ODE, we reduce the number of function evaluations while maintaining sample quality in function generation tasks, including applications to PDEs.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 39 of its 61 references that are in the map. First posted on arXiv 13 Mar 2025.

Builds on

39 of 61 references.

Closest ancestors · 21

Same direction, newest first

  1. 2023The probability flow ODE is provably fast19 May
  2. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation8 Mar
  3. 2023Consistency Models2 Mar
  4. 2023Continuous-Time Functional Diffusion Processes1 Mar
  5. 2023Infinite-Dimensional Diffusion Models20 Feb
  6. 2023Score-based Diffusion Models in Function Space14 Feb
  7. 2022Diffusion Generative Models in Infinite Dimensions1 Dec
  8. 2022Spectral Diffusion Processes28 Sep
  9. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  10. 2022Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matching16 Jun
  11. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  12. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
9 more
  1. 2022Riemannian Score-Based Generative Modelling6 Feb
  2. 2021Variational Diffusion Models1 Jul
  3. 2021Score-based Generative Modeling in Latent Space10 Jun
  4. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  5. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  6. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  7. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  8. 2020Denoising Diffusion Probabilistic Models19 Jun
  9. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 18

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  3. 2022Flow Matching for Generative Modelingcited by 5,702
  4. 2018Neural Ordinary Differential Equationscited by 3,779
  5. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  6. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  7. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  8. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 521
  9. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  10. 2023VideoFusion: Decomposed Diffusion Models for High-Quality Video Generationcited by 331
  11. 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 315
  12. 2021Score-based diffusion models for accelerated MRIcited by 311
6 more
  1. 2023Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion modelscited by 205
  2. 2023Functional Flow Matchingcited by 67
  3. 2023Diffusion-based Data Augmentation for Skin Disease Classification: Impact Across Original Medical Datasets to Fully Synthetic Imagescited by 45
  4. 2023Conditional score-based diffusion models for Bayesian inference in infinite dimensionscited by 38
  5. 2020A Kernel Two-Sample Test for Functional Datacited by 28
  6. 2024Masked Autoencoders are PDE Learnerscited by 14

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 4.

5 papers.

  1. 2025Flow Straight and Fast in Hilbert Space: Functional Rectified Flowcited by 6
  2. 2026Physics-informed diffusion models in spectral spacecited by 5
  3. 2026Topological Flow Matchingcited by 5
  4. 2026First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systemscited by 1
  5. 2026Discretization and Statistical Consistency of Functional Flow Matchingcited by 1

Similar, not cited

Close in wording, no citation either way

  1. 2026Probability flow ODEs in score-based and reflected diffusion models
  2. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models
  3. 2025Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models
  4. 2024Conditioning non-linear and infinite-dimensional diffusion processes
  5. 2024Stochastic Optimal Control for Diffusion Bridges in Function Spaces
  6. 2025Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models
  7. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances
  8. 2025FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modeling