mlsanityData to 14 Oct 2026

Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees

arXiv 2606.16610 ↗First posted 15 Jun 2026stat.ML cs.LGcited by 0

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

Abstract (arXiv)

Diffusion Flow Matching (DFM) has recently emerged as a versatile framework for generative modeling, yet its theoretical convergence properties remain only partially understood. In this work, we provide refined and novel convergence guarantees for Brownian motion based DFMs, focusing on the discretization error. Our analysis is conducted under the Kullback-Leibler (KL) divergence and the 2-Wasserstein distance. Under finite-moment conditions and a mild score integrability assumption, we derive KL convergence bounds with improved dimensional dependence compared to prior work, achieving, up to our knowledge, state-of-the-art scaling under minimal conditions. We further extend the analysis to the 2-Wasserstein distance: under an additional first-order score integrability assumption and a weak log-concavity condition, we obtain convergence guarantees with dimensional dependence consistent with the KL case.

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 35 of its 45 references that are in the map. First posted on arXiv 15 Jun 2026.

Builds on

35 of 45 references.

Closest ancestors · 8

Same direction, newest first

  1. 2025FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generation18 Aug
  2. 2024Flow Matching Guide and Code9 Dec
  3. 2024Theoretical guarantees in KL for Diffusion Flow Matching12 Sep
  4. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency models11 Jun
  5. 2023Generative Diffusion Models on Graphs: Methods and Applications6 Feb
  6. 2022Flow Matching for Generative Modeling6 Oct
  7. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transport29 Sep
  8. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 27

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  3. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  5. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  6. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  7. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  8. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  9. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 447
  10. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 445
  11. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptionscited by 219
  12. 2020MoFlow: An Invertible Flow Model for Generating Molecular Graphscited by 185
15 more
  1. 2023The probability flow ODE is provably fastcited by 146
  2. 2023Non-Denoising Forward-Time Diffusionscited by 77
  3. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptionscited by 63
  4. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Modelscited by 58
  5. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distancecited by 29
  6. 2024An analysis of the noise schedule for score-based generative modelscited by 27
  7. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimatescited by 25
  8. 2023Projected Langevin dynamics and a gradient flow for entropic optimal transportcited by 17
  9. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradientscited by 15
  10. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Boundscited by 9
  11. 2025Non-asymptotic error bounds for probability flow ODEs under weak log-concavitycited by 7
  12. 2025Wasserstein Convergence of Critically Damped Langevin Diffusionscited by 6
  13. 2025Finite-Time Analysis of Discrete-Time Stochastic Interpolantscited by 4
  14. 2025Pathway to O(√d) Complexity bound under Wasserstein metric of flow-based modelscited by 4
  15. 2025Exponential Convergence Guarantees for Iterative Markovian Fittingcited by 3

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2024Flow matching achieves almost minimax optimal convergence
  2. 2025On the minimax optimality of Flow Matching through the connection to kernel density estimation
  3. 2025Distribution estimation via Flow Matching with Lipschitz guarantees
  4. 2025A Sharp KL-Convergence Analysis for Diffusion Models under Minimal Assumptions
  5. 2025Theoretical Guarantees for High Order Trajectory Refinement in Generative Flows
  6. 2025On Flow Matching KL Divergence
  7. 2024Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences
  8. 2026Discrete Flow Matching: Convergence Guarantees Under Minimal Assumptions