# Flow Generator Matching

arXiv: https://arxiv.org/abs/2410.19310 · HTML: https://mlsanity.com/paper/2410.19310/

## Key facts

- Cited by 26 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 77 of its 84 references that are in the map.
- First posted on arXiv 25 Oct 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, 30 of 77)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignment](https://mlsanity.com/paper/2310.11513/) (2023)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [PixArt-α: Fast Training of Diffusion Transformer for Photorealistic Text-to-Image Synthesis](https://mlsanity.com/paper/2310.00426/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [DiffEdit: Diffusion-based semantic image editing with mask guidance](https://mlsanity.com/paper/2210.11427/) (2022)

## Built on by (most cited first, 26 of 26)

- [Self Forcing: Bridging the Train-Test Gap in Autoregressive Video Diffusion](https://mlsanity.com/paper/2506.08009/) (2025)
- [Schedule On the Fly: Diffusion Time Prediction for Faster and Better Image Generation](https://mlsanity.com/paper/2412.01243/) (2024)
- [Distributional Diffusion Models with Scoring Rules](https://mlsanity.com/paper/2502.02483/) (2025)
- [Phased DMD: Few-step Distribution Matching Distillation via Score Matching within Subintervals](https://mlsanity.com/paper/2510.27684/) (2025)
- [Self-Guidance: Boosting Flow and Diffusion Generation on Their Own](https://mlsanity.com/paper/2412.05827/) (2024)
- [Ultra-Fast Language Generation via Discrete Diffusion Divergence Instruct](https://mlsanity.com/paper/2509.25035/) (2025)
- [Inverse Bridge Matching Distillation](https://mlsanity.com/paper/2502.01362/) (2025)
- [Uni-Instruct: One-step Diffusion Model through Unified Diffusion Divergence Instruction](https://mlsanity.com/paper/2505.20755/) (2025)
- [Learning to Integrate Diffusion ODEs by Averaging the Derivatives](https://mlsanity.com/paper/2505.14502/) (2025)
- [Score Distillation of Flow Matching Models](https://mlsanity.com/paper/2509.25127/) (2025)
- [IDLM: Inverse-distilled Diffusion Language Models](https://mlsanity.com/paper/2602.19066/) (2026)
- [Soft-Di[M]O: Improving One-Step Discrete Image Generation with Soft Embeddings](https://mlsanity.com/paper/2509.22925/) (2025)
- [GenDR: Lighten Generative Detail Restoration](https://mlsanity.com/paper/2503.06790/) (2025)
- [Dimathtt[M]O: Distilling Masked Diffusion Models into One-step Generator](https://mlsanity.com/paper/2503.15457/) (2025)
- [Towards High-Order Mean Flow Generative Models: Feasibility, Expressivity, and Provably Efficient Criteria](https://mlsanity.com/paper/2508.07102/) (2025)
- [Universal Inverse Distillation for Matching Models with Real-Data Supervision (No GANs)](https://mlsanity.com/paper/2509.22459/) (2025)
- [FlowMotion: Target-Predictive Conditional Flow Matching for Jitter-Reduced Text-Driven Human Motion Generation](https://mlsanity.com/paper/2504.01338/) (2025)
- [Midpoint Generative Models](https://mlsanity.com/paper/2605.29920/) (2026)
- [One-Step Residual Shifting Diffusion for Image Super-Resolution via Distillation](https://mlsanity.com/paper/2503.13358/) (2025)
- [InstantViR: Real-Time Video Inverse Problem Solver with Distilled Diffusion Prior](https://mlsanity.com/paper/2511.14208/) (2025)
- [Overclocking Electrostatic Generative Models](https://mlsanity.com/paper/2509.22454/) (2025)
- [Ultra Fast PDE Solving via Physics Guided Few-step Diffusion](https://mlsanity.com/paper/2602.03627/) (2026)
- [Dive3D: Diverse Distillation-based Text-to-3D Generation via Score Implicit Matching](https://mlsanity.com/paper/2506.13594/) (2025)
- [Straight-Path Flow Matching for Incomplete Multi-View Clustering](https://mlsanity.com/paper/2607.06281/) (2026)
- [On the Inverse Flow Matching Problem in the One-Dimensional and Gaussian Cases](https://mlsanity.com/paper/2512.23265/) (2025)
- [Distribution Matching Distillation for Continuous Diffusion Language Models](https://mlsanity.com/paper/2609.40235/) (2026)

## Abstract (arXiv)

In the realm of Artificial Intelligence Generated Content (AIGC), flow-matching models have emerged as a powerhouse, achieving success due to their robust theoretical underpinnings and solid ability for large-scale generative modeling. These models have demonstrated state-of-the-art performance, but their brilliance comes at a cost. The process of sampling from these models is notoriously demanding on computational resources, as it necessitates the use of multi-step numerical ordinary differential equations (ODEs). Against this backdrop, this paper presents a novel solution with theoretical guarantees in the form of Flow Generator Matching (FGM), an innovative approach designed to accelerate the sampling of flow-matching models into a one-step generation, while maintaining the original performance. On the CIFAR10 unconditional generation benchmark, our one-step FGM model achieves a new record Fr'echet Inception Distance (FID) score of 3.08 among few-step flow-matching-based models, outperforming original 50-step flow-matching models. Furthermore, we use the FGM to distill the Stable Diffusion 3, a leading text-to-image flow-matching model based on the MM-DiT architecture. The resulting MM-DiT-FGM one-step text-to-image model demonstrates outstanding industry-level performance. When evaluated on the GenEval benchmark, MM-DiT-FGM has delivered remarkable generating qualities, rivaling other multi-step models in light of the efficiency of a single generation step.