# Exploring Diffusion and Flow Matching Under Generator Matching

arXiv: https://arxiv.org/abs/2412.11024 · HTML: https://mlsanity.com/paper/2412.11024/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 14 of its 17 references that are in the map.
- First posted on arXiv 15 Dec 2024.

## Placed in

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

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [Deep Generative Markov State Models](https://mlsanity.com/paper/1805.07601/) (2018)
- [ANT: Adaptive Noise Schedule for Time Series Diffusion Models](https://mlsanity.com/paper/2410.14488/) (2024)
- [Backstepping for Partial Differential Equations:A Survey](https://mlsanity.com/paper/2410.15146/) (2024)

## Built on by (most cited first, 9 of 9)

- [Scaling Image and Video Generation via Test-Time Evolutionary Search](https://mlsanity.com/paper/2505.17618/) (2025)
- [Angle Domain Guidance: Latent Diffusion Requires Rotation Rather Than Extrapolation](https://mlsanity.com/paper/2506.11039/) (2025)
- [Scale Where It Matters: Training-Free Localized Scaling for Diffusion Models](https://mlsanity.com/paper/2511.19917/) (2025)
- [Warm Starts Accelerate Conditional Diffusion](https://mlsanity.com/paper/2507.09212/) (2025)
- [RMFlow: Refined Mean Flow by a Noise-Injection Step for Multimodal Generation](https://mlsanity.com/paper/2602.00849/) (2026)
- [A-FloPS: Accelerating Diffusion Models via Adaptive Flow Path Sampler](https://mlsanity.com/paper/2509.00036/) (2025)
- [Tuning Real-World Image Restoration at Inference: A Test-Time Scaling Paradigm for Flow Matching Models](https://mlsanity.com/paper/2603.22027/) (2026)
- [A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models](https://mlsanity.com/paper/2605.06829/) (2026)
- [BridgeVoC: Revitalizing Neural Vocoder from a Restoration Perspective](https://mlsanity.com/paper/2511.07116/) (2025)

## Abstract (arXiv)

In this paper, we present a comprehensive theoretical comparison of diffusion and flow matching under the Generator Matching framework. Despite their apparent differences, both diffusion and flow matching can be viewed under the unified framework of Generator Matching. By recasting both diffusion and flow matching under the same generative Markov framework, we provide theoretical insights into why flow matching models can be more robust empirically and how novel model classes can be constructed by mixing deterministic and stochastic components. Our analysis offers a fresh perspective on the relationships between state-of-the-art generative modeling paradigms.