mlsanityData to 7 Oct 2026

Variational Flow Models: Flowing in Your Style

arXiv 2402.02977 ↗First posted 5 Feb 2024cs.LG cs.AIcited by 3

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

Abstract (arXiv)

We propose a systematic training-free method to transform the probability flow of a "linear" stochastic process characterized by the equation Xt=atX0+σtX1 into a straight constant-speed (SC) flow, reminiscent of Rectified Flow. This transformation facilitates fast sampling along the original probability flow via the Euler method without training a new model of the SC flow. The flexibility of our approach allows us to extend our transformation to inter-convert two posterior flows of two distinct linear stochastic processes. Moreover, we can easily integrate high-order numerical solvers into the transformed SC flow, further enhancing the sampling accuracy and efficiency. Rigorous theoretical analysis and extensive experimental results substantiate the advantages of our framework. Our code is available at this [https://github.com/clarken92/VFM||link].

Key facts. Cited by 3 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 38 of its 56 references that are in the map. First posted on arXiv 5 Feb 2024.

Builds on

38 of 56 references.

Closest ancestors · 5

Same direction, newest first

  1. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation12 Sep
  2. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplings28 Apr
  3. 2022Flow Matching for Generative Modeling6 Oct
  4. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transport29 Sep
  5. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 33

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  8. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  9. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  10. 2022Video Diffusion Modelscited by 2,280
  11. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
  12. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,903
21 more
  1. 2023Consistency Modelscited by 1,778
  2. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  3. 2021Variational Diffusion Modelscited by 1,145
  4. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  5. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  6. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Modelscited by 924
  7. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  8. 2022Pseudo Numerical Methods for Diffusion Models on Manifoldscited by 695
  9. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  10. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 635
  11. 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 526
  12. 2023UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Modelscited by 441
  13. 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speedcited by 344
  14. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Modelscited by 331
  15. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  16. 2017GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibriumcited by 208
  17. 2022Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Qualitycited by 181
  18. 2021On Fast Sampling of Diffusion Probabilistic Modelscited by 170
  19. 2021Learning to Efficiently Sample from Diffusion Probabilistic Modelscited by 129
  20. 2022Progressive Distillation for Fast Sampling of Diffusion Modelscited by 61
  21. 2022Maximum Likelihood Training of Implicit Nonlinear Diffusion Modelscited by 42

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025h-Edit: Effective and Flexible Diffusion-Based Editing via Doob's h-Transformcited by 18
  2. 2025Bidirectional Diffusion Bridge Modelscited by 8
  3. 2026Residual Diffusion Implicit Modelscited by 0

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  3. 2026Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspective
  4. 2025SCoT: Unifying Consistency Models and Rectified Flows via Straight-Consistent Trajectories
  5. 2025Rectified Flows for Fast Multiscale Fluid Flow Modeling
  6. 2024Improving the Training of Rectified Flows
  7. 2024Local Flow Matching Generative Models
  8. 2025Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models