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Flow Matching (FM) is an effective framework for training a model to learn a vector field that transports samples from a source distribution to a target distribution.
Gradient-based learning applied to document recognition
Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner · 1998
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Learning multiple layers of features from tiny images
Alex Krizhevsky, Geoffrey Hinton, et al · 2009
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Deep unsupervised learning using nonequilibrium thermodynamics
Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli · 2015
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Progressive growing of gans for improved quality, stability, and variation
Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen · 2017
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Denoising diffusion probabilistic models
Jonathan Ho, Ajay Jain, and Pieter Abbeel · 2020
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Denoising diffusion implicit models
Jiaming Song, Chenlin Meng, and Stefano Ermon · 2020
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Score-based generative modeling through stochastic differential equations
Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole · 2020
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Elucidating the design space of diffusion-based generative models
Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine · 2022
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Flow matching for generative modeling
Yaron Lipman, Ricky TQ Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le · 2022
Earlier work this paper cites.
Flow straight and fast: Learning to generate and transfer data with rectified flow
Xingchao Liu, Chengyue Gong, and Qiang Liu · 2022
Cited alongside, same era.
Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps
Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu · 2022
Cited alongside, same era.
Progressive distillation for fast sampling of diffusion models
Tim Salimans and Jonathan Ho · 2022
Cited alongside, same era.
Scalable diffusion models with transformers
William Peebles and Saining Xie · 2023
Cited alongside, same era.
Multisample flow matching: Straightening flows with minibatch couplings
Aram-Alexandre Pooladian, Heli Ben-Hamu, Carles Domingo-Enrich, Brandon Amos, Yaron Lipman, and Ricky TQ Chen · 2023
Flow matching for scalable simulation-based inference
Jonas Wildberger, Maximilian Dax, Simon Buchholz, Stephen Green, Jakob H Macke, and Bernhard Schölkopf · 2023
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Relational diffusion distillation for efficient image generation
Weilun Feng, Chuanguang Yang, Zhulin An, Libo Huang, Boyu Diao, Fei Wang, and Yongjun Xu · 2024
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One step diffusion via shortcut models
Kevin Frans, Danijar Hafner, Sergey Levine, and Pieter Abbeel · 2024
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Improving the training of rectified flows
Sangyun Lee, Zinan Lin, and Giulia Fanti · 2024
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Roformer: Enhanced transformer with rotary position embedding
Jianlin Su, Murtadha Ahmed, Yu Lu, Shengfeng Pan, Wen Bo, and Yunfeng Liu · 2024
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Rectified diffusion: Straightness is not your need in rectified flow
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Cited alongside, same era.
Consistency models
Yang Song, Prafulla Dhariwal, Mark Chen, and Ilya Sutskever · 2023
Cited alongside, same era.
Equivariant flow matching with hybrid probability transport for 3d molecule generation
Yuxuan Song, Jingjing Gong, Minkai Xu, Ziyao Cao, Yanyan Lan, Stefano Ermon, Hao Zhou, and Wei-Ying Ma · 2023
Cited alongside, same era.
Improving and generalizing flow-based generative models with minibatch optimal transport
Alexander Tong, Kilian Fatras, Nikolay Malkin, Guillaume Huguet, Yanlei Zhang, Jarrid Rector-Brooks, Guy Wolf, and Yoshua Bengio · 2023
Cited alongside, same era.
Alexander Tong, Nikolay Malkin, Kilian Fatras, Lazar Atanackovic, Yanlei Zhang, Guillaume Huguet, Guy Wolf, and Yoshua Bengio · 2023
Cited alongside, same era.
Fu-Yun Wang, Ling Yang, Zhaoyang Huang, Mengdi Wang, and Hongsheng Li · 2024
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Spatialvla: Exploring spatial representations for visual-language-action model, 2025
Delin Qu, Haoming Song, Qizhi Chen, Yuanqi Yao, Xinyi Ye, Yan Ding, Zhigang Wang, JiaYuan Gu, Bin Zhao, Dong Wang, and Xuelong Li · 2025
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Hume: Introducing system-2 thinking in visual-language-action model, 2025
Haoming Song, Delin Qu, Yuanqi Yao, Qizhi Chen, Qi Lv, Yiwen Tang, Modi Shi, Guanghui Ren, Maoqing Yao, Bin Zhao, Dong Wang, and Xuelong Li · 2025
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Towards hierarchical rectified flow
Yichi Zhang, Yici Yan, Alex Schwing, and Zhizhen Zhao · 2025
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