mlsanityData to 14 Oct 2026

Terminal Velocity Matching

arXiv 2511.19797 ↗First posted 24 Nov 2025cs.LG cs.AI cs.CVcited by 20

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

Abstract (arXiv)

We propose Terminal Velocity Matching (TVM), a generalization of flow matching that enables high-fidelity one- and few-step generative modeling. TVM models the transition between any two diffusion timesteps and regularizes its behavior at its terminal time rather than at the initial time. We prove that TVM provides an upper bound on the 2-Wasserstein distance between data and model distributions when the model is Lipschitz continuous. However, since Diffusion Transformers lack this property, we introduce minimal architectural changes that achieve stable, single-stage training. To make TVM efficient in practice, we develop a fused attention kernel that supports backward passes on Jacobian-Vector Products, which scale well with transformer architectures. On ImageNet-256x256, TVM achieves 3.29 FID with a single function evaluation (NFE) and 1.99 FID with 4 NFEs. It similarly achieves 4.32 1-NFE FID and 2.94 4-NFE FID on ImageNet-512x512, representing state-of-the-art performance for one/few-step models from scratch.

Key facts. Cited by 20 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 40 of its 45 references that are in the map. First posted on arXiv 24 Nov 2025.

Builds on

40 of 45 references.

Closest ancestors · 5

Same direction, newest first

  1. 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillation17 Jun
  2. 2025How to build a consistency model: Learning flow maps via self-distillation24 May
  3. 2024Physics Informed Distillation for Diffusion Models13 Nov
  4. 2022Flow Matching for Generative Modeling6 Oct
  5. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 35

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  3. 2023LLaMA: Open and Efficient Foundation Language Modelscited by 14,132
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  7. 2022Scalable Diffusion Models with Transformerscited by 6,054
  8. 2022Classifier-Free Diffusion Guidancecited by 5,847
  9. 2016Layer Normalizationcited by 5,669
  10. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesiscited by 4,356
  11. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,181
  12. 2022FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awarenesscited by 3,673
23 more
  1. 2025Wan: Open and Advanced Large-Scale Video Generative Modelscited by 2,708
  2. 2023Consistency Modelscited by 1,822
  3. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  4. 2024WorldSimBench: Towards Video Generation Models as World Simulatorscited by 881
  5. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 737
  6. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  7. 2025Mean Flows for One-step Generative Modelingcited by 561
  8. 2022All are Worth Words: A ViT Backbone for Diffusion Modelscited by 502
  9. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 459
  10. 2023Improved Techniques for Training Consistency Modelscited by 439
  11. 2023Simple diffusion: End-to-end diffusion for high resolution imagescited by 422
  12. 2023Analyzing and Improving the Training Dynamics of Diffusion Modelscited by 402
  13. 2024One Step Diffusion via Shortcut Modelscited by 391
  14. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentationcited by 304
  15. 2024Simplifying, Stabilizing and Scaling Continuous-Time Consistency Modelscited by 283
  16. 2020The Lipschitz Constant of Self-Attentioncited by 174
  17. 2018Online normalizer calculation for softmaxcited by 162
  18. 2025Inductive Moment Matchingcited by 113
  19. 2023How Smooth Is Attention?cited by 44
  20. 2023LipsFormer: Introducing Lipschitz Continuity to Vision Transformerscited by 34
  21. 2023Self-Consistent Velocity Matching of Probability Flowscited by 17
  22. 2025Visual Generation Without Guidancecited by 17
  23. 2025Learning to Integrate Diffusion ODEs by Averaging the Derivativescited by 10

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 20.

20 papers.

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By area:

  1. 2026Categorical Flow Mapscited by 44
  2. 2026Diamond Maps: Efficient Reward Alignment via Stochastic Flow Mapscited by 29
  3. 2026Riemannian MeanFlowcited by 8
  4. 2026Scaling Categorical Flow Mapscited by 8
  5. 2026Kernel-Gradient Drifting Modelscited by 7
  6. 2026How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidancecited by 6
  7. 2026Continuous Adversarial Flow Modelscited by 5
  8. 2026DiLaDiff: Distilled Latent-Augmented Diffusion for Language Modelingcited by 4
  9. 2026Amortized Moment Matching for Visual Generationcited by 2
  10. 2026Accelerating Diffusion Sampling via Speculative Draft Treescited by 2
  11. 2026FlashMol: High-Quality Molecule Generation in as Few as Four Stepscited by 1
  12. 2026WTF?! Simulation-Free Reinforcement Learning with Wasserstein-Tilted Flow Mapscited by 1
8 more
  1. 2026ReFPO: Reflow Regularization for Flow Matching Policy Gradientscited by 0
  2. 2026How I learned to stop worrying and love StopGrads: Stationarity, Convergence, and a case study on Flow Map Learningcited by 0
  3. 2026VTV-FM: Flow Matching through Variational Terminal-Velocity Closurecited by 0
  4. 2026Rank-Aware Speculative Sampling for Diffusion Draft Treescited by 0
  5. 2026Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamicscited by 0
  6. 2026Consistent Distribution Matching for Data-Free Diffusion Distillationcited by 0
  7. 2026Parametric Trajectory Distillation for Few-Step Video Generationcited by 0
  8. 2026Occupancy Modeling via Drifting: One-Step Generation Enables Direct Policy Extractioncited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025From Navigation to Refinement: Revealing the Two-Stage Nature of Flow-based Diffusion Models through Oracle Velocity
  2. 2026Temporal Pair Consistency for Variance-Reduced Flow Matching
  3. 2025Shortcutting Pre-trained Flow Matching Diffusion Models is Almost Free Lunch
  4. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency models
  5. 2024Reflected Flow Matching
  6. 2025Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching
  7. 2026ODE-free Neural Flow Matching for One-Step Generative Modeling
  8. 2025Theoretical Guarantees for High Order Trajectory Refinement in Generative Flows