mlsanityData to 7 Oct 2026

Variational Flow Matching for Graph Generation

arXiv 2406.04843 ↗First posted 7 Jun 2024cs.LG stat.MLcited by 78

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

Abstract (arXiv)

We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to implement, computationally efficient, and achieves strong results on graph generation tasks. In VFM, the objective is to approximate the posterior probability path, which is a distribution over possible end points of a trajectory. We show that VFM admits both the CatFlow objective and the original flow matching objective as special cases. We also relate VFM to score-based models, in which the dynamics are stochastic rather than deterministic, and derive a bound on the model likelihood based on a reweighted VFM objective. We evaluate CatFlow on one abstract graph generation task and two molecular generation tasks. In all cases, CatFlow exceeds or matches performance of the current state-of-the-art models.

Key facts. Cited by 78 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 53 of its 65 references that are in the map. First posted on arXiv 7 Jun 2024.

Builds on

53 of 65 references.

Closest ancestors · 14

Same direction, newest first

  1. 2024Dirichlet Flow Matching with Applications to DNA Sequence Design8 Feb
  2. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design7 Feb
  3. 2023Flow Matching in Latent Space17 Jul
  4. 2023Equivariant flow matching26 Jun
  5. 2023Flow Matching for Scalable Simulation-Based Inference26 May
  6. 2023Flow Matching on General Geometries7 Feb
  7. 2022Flow Matching for Generative Modeling6 Oct
  8. 2022DiGress: Discrete Denoising diffusion for graph generation29 Sep
  9. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep
  10. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem8 Jun
  11. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  12. 2022Flow-matching -- efficient coarse-graining of molecular dynamics without forces21 Mar
2 more
  1. 2022Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations5 Feb
  2. 2020Permutation Invariant Graph Generation via Score-Based Generative Modeling2 Mar

Other references · 39

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  6. 2018Neural Ordinary Differential Equationscited by 3,733
  7. 2015Variational Inference with Normalizing Flowscited by 2,161
  8. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  9. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  10. 2021Variational Diffusion Modelscited by 1,145
  11. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  12. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
27 more
  1. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  2. 2020A Generalization of Transformer Networks to Graphscited by 653
  3. 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 526
  4. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 406
  5. 2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 375
  6. 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 301
  7. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentationcited by 293
  8. 2022Diffsound: Discrete Diffusion Model for Text-to-sound Generationcited by 256
  9. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 231
  10. 2022Continuous diffusion for categorical datacited by 202
  11. 2018Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discoverycited by 191
  12. 2020MoFlow: An Invertible Flow Model for Generating Molecular Graphscited by 183
  13. 2018Constrained Graph Variational Autoencoders for Molecule Designcited by 182
  14. 2021GraphDF: A Discrete Flow Model for Molecular Graph Generationcited by 177
  15. 2022Generative Modelling With Inverse Heat Dissipationcited by 164
  16. 2023LayoutDM: Discrete Diffusion Model for Controllable Layout Generationcited by 141
  17. 2019GraphNVP: An Invertible Flow Model for Generating Molecular Graphscited by 115
  18. 2019Graph Normalizing Flowscited by 103
  19. 2022Soft Diffusion: Score Matching for General Corruptionscited by 101
  20. 2022SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generatorscited by 96
  21. 2022Blurring Diffusion Modelscited by 89
  22. 2021GraphEBM: Molecular Graph Generation with Energy-Based Modelscited by 85
  23. 2021Moser Flow: Divergence-based Generative Modeling on Manifoldscited by 67
  24. 2022Matching Normalizing Flows and Probability Paths on Manifoldscited by 57
  25. 2022Categorical SDEs with Simplex Diffusioncited by 42
  26. 2020Categorical Normalizing Flows via Continuous Transformationscited by 36
  27. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusionscited by 27

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 34; 2026: 40.

78 papers.

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  1. 2025Path Planning for Masked Diffusion Model Samplingcited by 79
  2. 2026Categorical Flow Mapscited by 37
  3. 2025Variational Rectified Flow Matchingcited by 34
  4. 2025Learning-Order Autoregressive Models with Application to Molecular Graph Generationcited by 29
  5. 2024Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Predictioncited by 28
  6. 2026LangFlow: Continuous Diffusion Rivals Discrete in Language Modelingcited by 28
  7. 2024Training Free Guided Flow Matching with Optimal Controlcited by 23
  8. 2026Discrete Flow Mapscited by 23
  9. 2025Graph Generative Pre-trained Transformercited by 16
  10. 2025Exponential Family Variational Flow Matching for Tabular Data Generationcited by 15
  11. 2025Flow Matching Meets Biology and Life Science: A Surveycited by 14
  12. 2024Exploring Discrete Flow Matching for 3D De Novo Molecule Generationcited by 11
38 more
  1. 2024Improving Molecular Graph Generation with Flow Matching and Optimal Transportcited by 10
  2. 2025Riemannian Variational Flow Matching for Material and Protein Designcited by 9
  3. 2025Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generationcited by 9
  4. 2025Controlled Generation with Equivariant Variational Flow Matchingcited by 9
  5. 2026Self-conditioned Flow Map Language Models via Fixed-point Flowscited by 9
  6. 2025Bures-Wasserstein Flow Matching for Graph Generationcited by 7
  7. 2025Modeling Microenvironment Trajectories on Spatial Transcriptomics with NicheFlowcited by 7
  8. 2025HOG-Diff: Higher-Order Guided Diffusion for Graph Generationcited by 6
  9. 2025BLIPs: Bayesian Learned Interatomic Potentialscited by 6
  10. 2025Flow Matching for Tabular Data Synthesiscited by 6
  11. 2026Scaling Categorical Flow Mapscited by 6
  12. 2026Kernel-Gradient Drifting Modelscited by 6
  13. 2026Thinking with Looped Flowscited by 6
  14. 2025BARNN: A Bayesian Autoregressive and Recurrent Neural Networkcited by 5
  15. 2025Devil is in the Details: Density Guidance for Detail-Aware Generation with Flow Modelscited by 5
  16. 2025FragFM: Hierarchical Framework for Efficient Molecule Generation via Fragment-Level Discrete Flow Matchingcited by 5
  17. 2025EgoTraj-Bench: Towards Robust Trajectory Prediction Under Ego-view Noisy Observationscited by 5
  18. 2025ProtFlow: Fast Protein Sequence Design via Flow Matching on Compressed Protein Language Model Embeddingscited by 4
  19. 2025RETRO SYNFLOW: Discrete Flow Matching for Accurate and Diverse Single-Step Retrosynthesiscited by 4
  20. 2025Purrception: Variational Flow Matching for Vector-Quantized Image Generationcited by 4
  21. 2025Graph-Conditional Flow Matching for Relational Data Generationcited by 3
  22. 2025GGBall: Graph Generative Model on Poincar'e Ballcited by 3
  23. 2025Generating Directed Graphs with Dual Attention and Asymmetric Encodingcited by 3
  24. 2025Flow Stochastic Segmentation Networkscited by 3
  25. 2025Diffusion Bridge or Flow Matching? A Unifying Framework and Comparative Analysiscited by 3
  26. 2025Simplex-to-Euclidean Bijections for Categorical Flow Matchingcited by 3
  27. 20263D Molecule Generation from Rigid Motifs via SE(3) Flowscited by 3
  28. 2026Prior-Informed Flow Matching for Graph Reconstructioncited by 3
  29. 2026TABES: Trajectory-Aware Backward-on-Entropy Steering for Masked Diffusion Modelscited by 3
  30. 2026Prediction--Loss Alignment for Sampler--Robust Flow Matching Trainingcited by 3
  31. 2026SDFlow: Similarity-Driven Flow Matching for Time Series Generationcited by 3
  32. 2026Forward-Learned Discrete Diffusion: Learning how to noise to denoise fastercited by 3
  33. 2026Flowette: Flow Matching with Graphette Priors for Graph Generationcited by 2
  34. 2026Graph-GRPO: Training Graph Flow Models with Reinforcement Learningcited by 2
  35. 2026Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generationcited by 2
  36. 2026Measuring the Dependency Gap: Diagnosing Inter-Column Fidelity in Tabular Generative Modelscited by 2
  37. 2025Graph Flow Matching: Enhancing Image Generation with Neighbor-Aware Flow Fieldscited by 1
  38. 2025GAGA: Gaussianity-Aware Gaussian Approximation for Efficient 3D Molecular Generationcited by 1

50 most cited of 78 All 78 (JSON)

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  1. 2025α-Flow: A Unified Framework for Continuous-State Discrete Flow Matching Models
  2. 2024DeFoG: Discrete Flow Matching for Graph Generation
  3. 2024Categorical Flow Matching on Statistical Manifolds
  4. 2026Latent Flow Matching for Molecular Graph Generation
  5. 2025Learning Straight Flows: Variational Flow Matching for Efficient Generation
  6. 2026Exploring and Exploiting Stability in Latent Flow Matching
  7. 2026Pawsterior: Variational Flow Matching for Structured Simulation-Based Inference
  8. 2024Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation