# Generator Matching: Generative modeling with arbitrary Markov processes

arXiv: https://arxiv.org/abs/2410.20587 · HTML: https://mlsanity.com/paper/2410.20587/

## Key facts

- Cited by 86 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- First posted on arXiv 27 Oct 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Built on by (most cited first, 30 of 86)

- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Edit Flows: Flow Matching with Edit Operations](https://mlsanity.com/paper/2506.09018/) (2025)
- [Any-Order Flexible Length Masked Diffusion](https://mlsanity.com/paper/2509.01025/) (2025)
- [Inference-Time Scaling for Flow Models via Stochastic Generation and Rollover Budget Forcing](https://mlsanity.com/paper/2503.19385/) (2025)
- [An Introduction to Flow Matching and Diffusion Models](https://mlsanity.com/paper/2506.02070/) (2025)
- [LEAPS: A discrete neural sampler via locally equivariant networks](https://mlsanity.com/paper/2502.10843/) (2025)
- [Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints](https://mlsanity.com/paper/2506.08604/) (2025)
- [Variational Control for Guidance in Diffusion Models](https://mlsanity.com/paper/2502.03686/) (2025)
- [Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spaces](https://mlsanity.com/paper/2506.07903/) (2025)
- [DiFFPO: Training Diffusion LLMs to Reason Fast and Furious via Reinforcement Learning](https://mlsanity.com/paper/2510.02212/) (2025)
- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [OneFlow: Concurrent Mixed-Modal and Interleaved Generation with Edit Flows](https://mlsanity.com/paper/2510.03506/) (2025)
- [Exponential Family Variational Flow Matching for Tabular Data Generation](https://mlsanity.com/paper/2506.05940/) (2025)
- [The Diffusion Duality, Chapter II: Psi-Samplers](https://mlsanity.com/paper/2602.21185/) (2026)
- [Transition Matching: Scalable and Flexible Generative Modeling](https://mlsanity.com/paper/2506.23589/) (2025)
- [Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics](https://mlsanity.com/paper/2512.00580/) (2025)
- [Diffusion Models in Simulation-Based Inference: A Tutorial Review](https://mlsanity.com/paper/2512.20685/) (2025)
- [Discrete Adjoint Matching](https://mlsanity.com/paper/2602.07132/) (2026)
- [Exploring Diffusion and Flow Matching Under Generator Matching](https://mlsanity.com/paper/2412.11024/) (2024)
- [Error Analysis of Discrete Flow with Generator Matching](https://mlsanity.com/paper/2509.21906/) (2025)
- [Telegrapher's Generative Model via Kac Flows](https://mlsanity.com/paper/2506.20641/) (2025)
- [Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modeling](https://mlsanity.com/paper/2602.20210/) (2026)
- [The Spacetime of Diffusion Models: An Information Geometry Perspective](https://mlsanity.com/paper/2505.17517/) (2025)
- [Discrete Guidance Matching: Exact Guidance for Discrete Flow Matching](https://mlsanity.com/paper/2509.21912/) (2025)
- [Spherical Flows for Sampling Categorical Data](https://mlsanity.com/paper/2605.05629/) (2026)
- [Strong Stochastic Flow Maps](https://mlsanity.com/paper/2606.01086/) (2026)
- [Stiefel Flow Matching for Moment-Constrained Structure Elucidation](https://mlsanity.com/paper/2412.12540/) (2024)
- [Generative modelling with jump-diffusions](https://mlsanity.com/paper/2503.06558/) (2025)
- [Universal Inverse Distillation for Matching Models with Real-Data Supervision (No GANs)](https://mlsanity.com/paper/2509.22459/) (2025)
- [Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions](https://mlsanity.com/paper/2511.09465/) (2025)

## 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.