mlsanityData to 7 Oct 2026

Variational Rectified Flow Matching

arXiv 2502.09616 ↗First posted 13 Feb 2025cs.LG cs.CVcited by 34

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

Abstract (arXiv)

We study Variational Rectified Flow Matching, a framework that enhances classic rectified flow matching by modeling multi-modal velocity vector-fields. At inference time, classic rectified flow matching 'moves' samples from a source distribution to the target distribution by solving an ordinary differential equation via integration along a velocity vector-field. At training time, the velocity vector-field is learnt by linearly interpolating between coupled samples one drawn from the source and one drawn from the target distribution randomly. This leads to ''ground-truth'' velocity vector-fields that point in different directions at the same location, i.e., the velocity vector-fields are multi-modal/ambiguous. However, since training uses a standard mean-squared-error loss, the learnt velocity vector-field averages ''ground-truth'' directions and isn't multi-modal. In contrast, variational rectified flow matching learns and samples from multi-modal flow directions. We show on synthetic data, MNIST, CIFAR-10, and ImageNet that variational rectified flow matching leads to compelling results.

Key facts. Cited by 34 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 8 of its 33 references that are in the map. First posted on arXiv 13 Feb 2025.

Builds on

8 of 33 references.

Closest ancestors · 3

Same direction, newest first

  1. 2024Consistency Flow Matching: Defining Straight Flows with Velocity Consistency2 Jul
  2. 2024Variational Flow Matching for Graph Generation7 Jun
  3. 2024PeRFlow: Piecewise Rectified Flow as Universal Plug-and-Play Accelerator13 May

Other references · 5

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  3. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 707
  4. 2022Understanding Diffusion Models: A Unified Perspectivecited by 337
  5. 2022DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latentscited by 103

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 13; 2026: 21.

34 papers.

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  1. 2025Towards Hierarchical Rectified Flowcited by 19
  2. 2025The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generationcited by 16
  3. 2025Adversarial Flow Modelscited by 10
  4. 2025VFP: Variational Flow-Matching Policy for Multi-Modal Robot Manipulationcited by 9
  5. 2025Learning Straight Flows: Variational Flow Matching for Efficient Generationcited by 7
  6. 2025Efficient Flow Matching using Latent Variablescited by 6
  7. 2025Hierarchical Rectified Flow Matching with Mini-Batch Couplingscited by 6
  8. 2025Quantum Flow Matchingcited by 4
  9. 2025Variational Masked Diffusion Modelscited by 4
  10. 2026Training-Free Refinement of Flow Matching with Divergence-based Samplingcited by 4
  11. 2026A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimationcited by 3
  12. 2025FlowSynth: Instrument Generation Through Distributional Flow Matching and Test-Time Searchcited by 2
22 more
  1. 2026Temporal Pair Consistency for Variance-Reduced Flow Matchingcited by 2
  2. 2026Variational Grey-Box Dynamics Matchingcited by 2
  3. 2025Coupled Flow Matchingcited by 1
  4. 2025FlowDet: Unifying Object Detection and Generative Transport Flowscited by 1
  5. 2026CaReFlow: Cyclic Adaptive Rectified Flow for Multimodal Fusioncited by 1
  6. 2026Transition Flow Matchingcited by 1
  7. 2026DiReCT: Disentangled Regularization of Contrastive Trajectories for Physics-Refined Video Generationcited by 1
  8. 2026MixFlow: Mixed Source Distributions Improve Rectified Flowscited by 1
  9. 2026Second Order Drifting Modelscited by 1
  10. 2025Risk-Entropic Flow Matchingcited by 0
  11. 2026Communication-Inspired Tokenization for Structured Image Representationscited by 0
  12. 2026Uncovering Physical Drivers of Dark Matter Halo Structures with Auxiliary-Variable-Guided Generative Modelscited by 0
  13. 2026Towards Faster Language Model Inference Using Mixture-of-Experts Flow Matchingcited by 0
  14. 2026Structured Coupling for Flow Matchingcited by 0
  15. 2026Coreset-Induced Conditional Velocity Flow Matchingcited by 0
  16. 2026The Reverse Telescoping Coordinate System for Positive Definite Matrices: Geometry, Computation, and Generative Modelingcited by 0
  17. 2026Field Codes for Distributed Coupling Samplers and Certified Empirical Transportcited by 0
  18. 2026TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamicscited by 0
  19. 2026Climate Physics Dynamic Matchingcited by 0
  20. 2026Beyond Straightness: Non-Crossing Flow Matching via Quantile AlignTree Couplingcited by 0
  21. 2026ReaFlow-TTS: Realization-Conditioned Flow Matching for High-Quality and Controllable Speech Synthesiscited by 0
  22. 2026Variational Streaming Flow: Probabilistic Forecasting in Physical Timecited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Stable Velocity: A Variance Perspective on Flow Matching
  2. 2026Posterior Augmented Flow Matching
  3. 2024Reflected Flow Matching
  4. 2025VeCoR -- Velocity Contrastive Regularization for Flow Matching
  5. 2026VTV-FM: Flow Matching through Variational Terminal-Velocity Closure
  6. 2026A Theory on Flow Matching with Neural Networks
  7. 2026Smoother Flow Matching via Contrastive Trajectory Repulsion
  8. 2026AREX: Affine-Residual Exponential Integrator for Few-Step Sampling in Flow Matching