mlsanityData to 7 Oct 2026

Convergence Analysis of Flow Matching in Latent Space with Transformers

arXiv 2404.02538 ↗First posted 3 Apr 2024stat.ML cs.LGcited by 16

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

Abstract (arXiv)

We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a transformer network is trained to predict the velocity field of the transformation from a standard normal distribution to the target latent distribution. Our error analysis demonstrates the effectiveness of this approach, showing that the distribution of samples generated via estimated ODE flow converges to the target distribution in the Wasserstein-2 distance under mild and practical assumptions. Furthermore, we show that arbitrary smooth functions can be effectively approximated by transformer networks with Lipschitz continuity, which may be of independent interest.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 41 of its 80 references that are in the map. First posted on arXiv 3 Apr 2024.

Builds on

41 of 80 references.

Closest ancestors · 2

Same direction, newest first

  1. 2023Flow Matching in Latent Space17 Jul
  2. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 39

  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. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  7. 2023Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasetscited by 2,526
  8. 2017Improved Training of Wasserstein GANscited by 2,223
  9. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  10. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,903
  11. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  12. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
27 more
  1. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  2. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  3. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  4. 2024VideoCrafter2: Overcoming Data Limitations for High-Quality Video Diffusion Modelscited by 568
  5. 2023VideoComposer: Compositional Video Synthesis with Motion Controllabilitycited by 461
  6. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 445
  7. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 440
  8. 2019Are Transformers universal approximators of sequence-to-sequence functions?cited by 404
  9. 2022Convergence of denoising diffusion models under the manifold hypothesiscited by 237
  10. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localizationcited by 230
  11. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptionscited by 215
  12. 2022Convergence of score-based generative modeling for general data distributionscited by 179
  13. 2022Convergence for score-based generative modeling with polynomial complexitycited by 176
  14. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Datacited by 171
  15. 2018Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionalitycited by 160
  16. 2023Diffusion Models are Minimax Optimal Distribution Estimatorscited by 159
  17. 2021Deep Generative Learning via Schr"odinger Bridgecited by 103
  18. 2022Poisson Flow Generative Modelscited by 95
  19. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptionscited by 61
  20. 2021An error analysis of generative adversarial networks for learning distributionscited by 35
  21. 2019Chart Auto-Encoders for Manifold Structured Datacited by 32
  22. 2018Approximability of Discriminators Implies Diversity in GANscited by 28
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  24. 2023Gaussian Interpolation Flowscited by 17
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  26. 2024Deep conditional distribution learning via conditional F"ollmer flowcited by 9
  27. 2023On the rate of convergence of an over-parametrized Transformer classifier learned by gradient descentcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 6; 2025: 7; 2026: 3.

16 papers.

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  1. 2024Learning stochastic dynamics from snapshots through regularized unbalanced optimal transportcited by 30
  2. 2024Flow matching achieves almost minimax optimal convergencecited by 27
  3. 2024On Statistical Rates of Conditional Diffusion Transformers: Approximation, Estimation and Minimax Optimalitycited by 21
  4. 2025A Theoretical Analysis of Discrete Flow Matching Generative Modelscited by 13
  5. 2024Latent Schr"odinger Bridge Diffusion Model for Generative Learningcited by 10
  6. 2025Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysiscited by 9
  7. 2024Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplerscited by 6
  8. 2025Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspectivecited by 5
  9. 2025On Flow Matching KL Divergencecited by 5
  10. 2025Approximation Bounds for Transformer Networks with Application to Regressioncited by 4
  11. 2024Model Free Prediction with Uncertainty Assessmentcited by 3
  12. 2025On Conditional Stochastic Interpolation for Generative Nonlinear Sufficient Dimension Reductioncited by 2
4 more
  1. 2025A Theory for Conditional Generative Modeling on Multiple Data Sourcescited by 1
  2. 2026Conditional Flow-VAE for Safety-Critical Traffic Scenario Generationcited by 0
  3. 2026Approximation Error Upper and Lower Bounds for H"older Class with Transformerscited by 0
  4. 2026Semi-Supervised Conditional Generative Learning through Stochastic Interpolation and Sufficient Representationscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026From Euler to Dormand-Prince: ODE Solvers for Flow Matching Generative Models
  2. 2025Theoretical Guarantees for High Order Trajectory Refinement in Generative Flows
  3. 2025Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching
  4. 2026ODE-free Neural Flow Matching for One-Step Generative Modeling
  5. 2022Flow Matching for Generative Modeling
  6. 2024Local Flow Matching Generative Models
  7. 2024Explicit Flow Matching: On The Theory of Flow Matching Algorithms with Applications
  8. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency models