mlsanityData to 7 Oct 2026

Generator Matching: Generative modeling with arbitrary Markov processes

arXiv 2410.20587 ↗First posted 27 Oct 2024cs.LG cs.AIcited by 82

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

Abstract (arXiv)

We introduce Generator Matching, a modality-agnostic framework for generative modeling using arbitrary Markov processes. Generators characterize the infinitesimal evolution of a Markov process, which we leverage for generative modeling in a similar vein to flow matching: we construct conditional generators which generate single data points, then learn to approximate the marginal generator which generates the full data distribution. We show that Generator Matching unifies various generative modeling methods, including diffusion models, flow matching and discrete diffusion models. Furthermore, it expands the design space to new and unexplored Markov processes such as jump processes. Finally, Generator Matching enables the construction of superpositions of Markov generative models and enables the construction of multimodal models in a rigorous manner. We empirically validate our method on image and multimodal generation, e.g. showing that superposition with a jump process improves performance.

Key facts. Cited by 82 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. First posted on arXiv 27 Oct 2024.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 40; 2026: 40.

82 papers.

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  1. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
  2. 2025Edit Flows: Flow Matching with Edit Operationscited by 53
  3. 2025Any-Order Flexible Length Masked Diffusioncited by 48
  4. 2025Inference-Time Scaling for Flow Models via Stochastic Generation and Rollover Budget Forcingcited by 37
  5. 2025An Introduction to Flow Matching and Diffusion Modelscited by 33
  6. 2025LEAPS: A discrete neural sampler via locally equivariant networkscited by 30
  7. 2025Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraintscited by 26
  8. 2025Variational Control for Guidance in Diffusion Modelscited by 22
  9. 2025Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spacescited by 19
  10. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  11. 2025DiFFPO: Training Diffusion LLMs to Reason Fast and Furious via Reinforcement Learningcited by 17
  12. 2025OneFlow: Concurrent Mixed-Modal and Interleaved Generation with Edit Flowscited by 17
38 more
  1. 2025Exponential Family Variational Flow Matching for Tabular Data Generationcited by 15
  2. 2026The Diffusion Duality, Chapter II: Psi-Samplerscited by 12
  3. 2025Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamicscited by 11
  4. 2025Transition Matching: Scalable and Flexible Generative Modelingcited by 10
  5. 2026Discrete Adjoint Matchingcited by 10
  6. 2024Exploring Diffusion and Flow Matching Under Generator Matchingcited by 9
  7. 2025Error Analysis of Discrete Flow with Generator Matchingcited by 9
  8. 2025Diffusion Models in Simulation-Based Inference: A Tutorial Reviewcited by 8
  9. 2025Telegrapher's Generative Model via Kac Flowscited by 7
  10. 2025The Spacetime of Diffusion Models: An Information Geometry Perspectivecited by 6
  11. 2025Discrete Guidance Matching: Exact Guidance for Discrete Flow Matchingcited by 6
  12. 2024Stiefel Flow Matching for Moment-Constrained Structure Elucidationcited by 5
  13. 2026Topological Flow Matchingcited by 5
  14. 2025Bit-Level Discrete Diffusion with Markov Probabilistic Models: An Improved Framework with Sharp Convergence Bounds under Minimal Assumptionscited by 4
  15. 2025Generative modelling with jump-diffusionscited by 4
  16. 2025Universal Inverse Distillation for Matching Models with Real-Data Supervision (No GANs)cited by 4
  17. 2025Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletionscited by 4
  18. 2025OXtal: An All-Atom Diffusion Model for Organic Crystal Structure Predictioncited by 4
  19. 2026Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modelingcited by 4
  20. 2026Spherical Flows for Sampling Categorical Datacited by 4
  21. 2026Strong Stochastic Flow Mapscited by 4
  22. 2025Energy-based generator matching: A neural sampler for general state spacecited by 3
  23. 2026Corrected Samplers for Discrete Flow Modelscited by 3
  24. 2026Count Bridges enable Modeling and Deconvolving Transcriptomic Datacited by 3
  25. 2026Riemannian MeanFlow for One-Step Generation on Manifoldscited by 3
  26. 2025Greed is Good: A Unifying Perspective on Guided Generationcited by 2
  27. 2025INFO-SEDD: Continuous Time Markov Chains as Scalable Information Metrics Estimatorscited by 2
  28. 2025A Jump-Diffusion Framework for Irregular Time Series Generationcited by 2
  29. 2025Deep Neural Networks Inspired by Differential Equationscited by 2
  30. 2025Time dependent loss reweighting for flow matching and diffusion models is theoretically justifiedcited by 2
  31. 2025Flowception: Temporally Expansive Flow Matching for Video Generationcited by 2
  32. 2025On Conditional Stochastic Interpolation for Generative Nonlinear Sufficient Dimension Reductioncited by 2
  33. 2026Inverting Data Transformations via Diffusion Samplingcited by 2
  34. 2026CountsDiff: A Diffusion Model on the Natural Numbers for Generation and Imputation of Count-Based Datacited by 2
  35. 2026Flow Matching for Count Datacited by 2
  36. 2026Generative Molecular Morphing for Flexible-Size Design via Unbalanced Optimal Transportcited by 2
  37. 2025Corrector Sampling in Language Modelscited by 1
  38. 2025Multimodal Generative Flows for LHC Jetscited by 1

50 most cited of 82 All 82 (JSON)

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  1. 2026Latent Process Generator Matching
  2. 2025Exploring the Design Space of Transition Matching
  3. 2026Context-weighted Discrete Flow Matching
  4. 2026Simulation-free and finite-time diffusion model
  5. 2026A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models
  6. 2025The Generation Phases of Flow Matching: a Denoising Perspective
  7. 2025Iterative Flow Matching: Path Correction and Gradual Refinement for Enhanced Generative Modeling
  8. 2026Notes on generative modeling: flow matching, diffusion, optimal transport and Schr"odinger bridge