mlsanityData to 14 Oct 2026

On Flow Matching KL Divergence

arXiv 2511.05480 ↗First posted 7 Nov 2025cs.LG cs.AI cs.CVcited by 6

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

Abstract (arXiv)

We derive a deterministic, non-asymptotic upper bound on the Kullback-Leibler (KL) divergence of the flow-matching distribution approximation. In particular, if the L2 flow-matching loss is bounded by ε2 > 0, then the KL divergence between the true data distribution and the estimated distribution is bounded by A1 ε + A2 ε2. Here, the constants A1 and A2 depend only on the regularities of the data and velocity fields. Consequently, this bound implies statistical convergence rates of Flow Matching Transformers under the Total Variation (TV) distance. We show that, flow matching achieves nearly minimax-optimal efficiency in estimating smooth distributions. Our results make the statistical efficiency of flow matching comparable to that of diffusion models under the TV distance. Numerical studies on synthetic and learned velocities corroborate our theory.

Key facts. Cited by 6 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 27 of its 32 references that are in the map. First posted on arXiv 7 Nov 2025.

Builds on

27 of 32 references.

Closest ancestors · 8

Same direction, newest first

  1. 2025A Theoretical Analysis of Discrete Flow Matching Generative Models26 Sep
  2. 2025On the minimax optimality of Flow Matching through the connection to kernel density estimation17 Apr
  3. 2024Flow Matching Guide and Code9 Dec
  4. 2024Theoretical guarantees in KL for Diffusion Flow Matching12 Sep
  5. 2024Flow matching achieves almost minimax optimal convergence31 May
  6. 2024Convergence Analysis of Flow Matching in Latent Space with Transformers3 Apr
  7. 2022Flow Matching for Generative Modeling6 Oct
  8. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 19

  1. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  2. 2022Scalable Diffusion Models with Transformerscited by 6,054
  3. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,885
  4. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,181
  5. 2018Neural Ordinary Differential Equationscited by 3,779
  6. 2015Trust Region Policy Optimizationcited by 2,580
  7. 2024π0: A Vision-Language-Action Flow Model for General Robot Controlcited by 2,407
  8. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  9. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  10. 2024Movie Gen: A Cast of Media Foundation Modelscited by 644
  11. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 445
  12. 2023Voicebox: Text-Guided Multilingual Universal Speech Generation at Scalecited by 379
7 more
  1. 2018Maximum a Posteriori Policy Optimisationcited by 328
  2. 2022Convergence of denoising diffusion models under the manifold hypothesiscited by 242
  3. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 119
  4. 2023Error Bounds for Flow Matching Methodscited by 91
  5. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Modelscited by 85
  6. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theorycited by 63
  7. 2024On Statistical Rates of Conditional Diffusion Transformers: Approximation, Estimation and Minimax Optimalitycited by 22

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 6.

6 papers.

  1. 2026Total Variation Rates for Riemannian Flow Matchingcited by 2
  2. 2026Morphologically Equivariant Flow Matching for Bimanual Mobile Manipulationcited by 0
  3. 2026Let the Dynamics Flow: Stable Flow Matching Dynamical Systemscited by 0
  4. 2026Drift Variation Autoencoder: Unifying Generation and Representation Learning through Conditional Posterior Flow Matchingcited by 0
  5. 2026Counterfactual Generation via Flow Matching: Coupling-Sensitive End-to-End Ratescited by 0
  6. 2026Primal-Dual Flow Matching for Sample-Wise Constrained Generationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees
  2. 2026Discrete Flow Matching: Convergence Guarantees Under Minimal Assumptions
  3. 2025Distribution estimation via Flow Matching with Lipschitz guarantees
  4. 2026Same Flow, Different Paths: Variance Reduction in Flow Matching
  5. 2025On The Hidden Biases of Flow Matching Samplers
  6. 2025Theoretical Guarantees for High Order Trajectory Refinement in Generative Flows
  7. 2026Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Support
  8. 2025Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching