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A summary of related works about flow matching, stochastic interpolants

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Awesome Flow Matching ( Stochastic Interpolant )

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Contributors

Papers

Flow Matching for Generative Modeling
Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, Matt Le
ICLR 2023. [Paper]
10 Oct 2022

Building Normalizing Flows with Stochastic Interpolants
Michael S. Albergo and Eric Vanden-Eijnden
ICLR 2023. [Paper]
Sept 2022

Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden
Arxiv 2023. [Paper]
March 2023

Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
Xingchao Liu, Chengyue Gong, Qiang Liu
ICLR 2023. [Paper]
Sep 2022

Minimizing trajectory curvature of ode-based generative models
Sangyun Lee, Beomsu Kim, Jong Chul Ye
ICML 2023. [Paper]
Jan 2023

Multisample Flow Matching: Straightening Flows with Minibatch Couplings
Aram-Alexandre Pooladian, Heli Ben-Hamu, Carles Domingo-Enrich, Brandon Amos, Yaron Lipman, Ricky T. Q. Chen
Arxiv Apr 2023. [Paper]

Neural Diffusion Models
Grigory Bartosh, Dmitry Vetrov, Christian A. Naesseth
ICML 2024. [Paper]

On Kinetic Optimal Probability Paths for Generative Models
Neta Shaul, Ricky T. Q. Chen, Maximilian Nickel, Matt Le, Yaron Lipman
Arxiv June 2023. [Paper]

Bellman Optimal Stepsize Straightening of Flow-Matching Models
Bao Nguyen, Binh Nguyen, Viet Anh Nguyen
ICLR 2024. [Paper]

Action Matching: Learning Stochastic Dynamics from Samples
Kirill Neklyudov, Rob Brekelmans, Daniel Severo, Alireza Makhzani
ICML 2023. [Paper]
Oct 2022

Stochastic Interpolants with Data-Dependent Couplings
Michael S. Albergo, Mark Goldstein, Nicholas M. Boffi, Rajesh Ranganath, Eric Vanden-Eijnden
ICML 2024. [Paper]

Error Bounds for Flow Matching Methods
Joe Benton, George Deligiannidis, Arnaud Doucet
Arxiv 2023. [Paper]

Flow Map Matching
Nicholas M. Boffi, Michael S. Albergo, Eric Vanden-Eijnden
Arxiv 2024. [Paper]

Functional Flow Matching
Gavin Kerrigan, Giosue Migliorini, Padhraic Smyth
Arxiv May 2023. [Paper]

Metric Flow Matching for Smooth Interpolations on the Data Manifold
Kacper Kapusniak, Peter Potaptchik, Teodora Reu, Leo Zhang, Alexander Tong, Michael Bronstein, Avishek Joey Bose, Francesco Di Giovanni
Arxiv May 2023. [Paper]

Unlocking Guidance for Discrete State-Space Diffusion and Flow Models
Hunter Nisonoff, Junhao Xiong, Stephan Allenspach, Jennifer Listgarten
Arxiv 2024. [Paper]

Variational Schrödinger Diffusion Models
Wei Deng, Weijian Luo, Yixin Tan, Marin Biloš, Yu Chen, Yuriy Nevmyvaka, Ricky T. Q. Chen
ICML 2024. [Paper]

Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling
Grigory Bartosh, Dmitry Vetrov, Christian A. Naesseth
Arxiv April 2024. [Paper]

Align Your Steps: Optimizing Sampling Schedules in Diffusion Models
Amirmojtaba Sabour, Sanja Fidler, Karsten Kreis
Arxiv April 2024. [Paper]

Multidimensional Interpolants\ Dohoon Lee, Kyogu Lee
Arxiv April 2024. [Paper]

Discrete Flow Matching
Itai Gat, Tal Remez, Neta Shaul, Felix Kreuk, Ricky T. Q. Chen, Gabriel Synnaeve, Yossi Adi, Yaron Lipman
Arxiv July 2024. [Paper]

Theory

Explicit Flow Matching: On The Theory of Flow Matching Algorithms with Applications
Gleb Ryzhakov, Svetlana Pavlova, Egor Sevriugov, Ivan Oseledets
Arxiv 2024. [Paper]

Flow matching achieves minimax optimal convergence
Kenji Fukumizu, Taiji Suzuki, Noboru Isobe, Kazusato Oko, Masanori Koyama
Arxiv 2405. [Paper]

Improving the Training of Rectified Flows
Sangyun Lee, Zinan Lin, Giulia Fanti
Arxiv 2405. [Paper]

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, Yoshua Bengio
TMLR 2024. [Paper]

Denoising Diffusion Bridge Models
Linqi Zhou, Aaron Lou, Samar Khanna, Stefano Ermon
ICLR 24. [Paper]

Extended Flow Matching: a Method of Conditional Generation with Generalized Continuity Equation
Noboru Isobe, Masanori Koyama, Kohei Hayashi, Kenji Fukumizu
Arxiv 2402. [Paper]

Bespoke Solvers for Generative Flow Models
Neta Shaul, Juan Perez, Ricky T. Q. Chen, Ali Thabet, Albert Pumarola, Yaron Lipman
Arxiv 2023. [Paper]

Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEs
Kaiwen Zheng, Cheng Lu, Jianfei Chen, Jun Zhu
ICML 2023. [Paper]
May 2023

Minimizing Trajectory Curvature of ODE-based Generative Models
Sangyun Lee, Beomsu Kim, Jong Chul Ye
arXiv 2023. [Paper]
Jan 2023

Self-Consistent Velocity Matching of Probability Flows
Lingxiao Li, Samuel Hurault, Justin Solomon
arXiv 2023. [Paper]
22 Feb 2023

Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden
arXiv 2023. [Paper]
15 Mar 2023

Interpretable ODE-style Generative Diffusion Model via Force Field Construction
Weiyang Jin, Yongpei Zhu, Yuxi Peng
arXiv 2023. [Paper]
15 Mar 2023

Generative Diffusions in Augmented Spaces: A Complete Recipe
Kushagra Pandey, Stephan Mandt
arXiv 2023. [Paper]
3 Mar 2023

A theory of continuous generative flow networks
Salem Lahlou, Tristan Deleu, Pablo Lemos, Dinghuai Zhang, Alexandra Volokhova, Alex Hernández-García, Léna Néhale Ezzine, Yoshua Bengio, Nikolay Malkin
arXiv 2023. [Paper,Code]
30 Jan 2023

Diffusion Schrödinger Bridge Matching
Yuyang Shi, Valentin De Bortoli, Andrew Campbell, Arnaud Doucet
Arxiv March 2023. [Paper]

Aligned Diffusion Schrödinger Bridges
Vignesh Ram Somnath, Matteo Pariset, Ya-Ping Hsieh, Maria Rodriguez Martinez, Andreas Krause, Charlotte Bunne
UAI 2023. [Paper]

Optimal Flow Matching: Learning Straight Trajectories in Just One Step
Nikita Kornilov, Alexander Gasnikov, Alexander Korotin
Arxiv 2403. [Paper]

Simplified Diffusion Schrödinger Bridge
Zhicong Tang, Tiankai Hang, Shuyang Gu, Dong Chen, Baining Guo
Arxiv 2403. [Paper]

Switched Flow Matching: Eliminating Singularities via Switching ODEs
Qunxi Zhu, Wei Lin
ICML 2024. [Paper]

Schrödinger Bridge

Unbalanced Diffusion Schrödinger Bridge
Matteo Pariset, Ya-Ping Hsieh, Charlotte Bunne, Andreas Krause, Valentin De Bortoli
Arxiv June 2024. [Paper]

Diffusion Bridge Mixture Transports, Schrödinger Bridge Problems and Generative Modeling
Stefano Peluchetti
JMLR (2023). [Paper]

Learning Diffusion Bridges on Constrained Domains
Xingchao Liu, Lemeng Wu, Mao Ye, qiang liu
ICLR 2023. [Paper]

Image-to-Image Schrödinger Bridge
Guan-Horng Liu, Arash Vahdat, De-An Huang, Evangelos Theodorou, Weili Nie, Anima Anandkumar
ICML 2023. [Paper]

On Schrödinger Bridge Matching and Expectation Maximization
Rob Brekelmans, Kirill Neklyudov
OTML 2023. [Paper]

Light and Optimal Schrödinger Bridge Matching
Nikita Gushchin, Sergei Kholkin, Evgeny Burnaev, Alexander Korotin
ICML 2024. [Paper]

Fast Ensembling with Diffusion Schrödinger Bridge
Hyunsu Kim, Jongmin Yoon, Juho Lee
ICLR 2024. [Paper]

Generalized Schrödinger Bridge Matching
Guan-Horng Liu, Yaron Lipman, Maximilian Nickel, Brian Karrer, Evangelos Theodorou, Ricky T. Q. Chen
ICLR 2024. [Paper]

Light Schrödinger Bridge
Alexander Korotin, Nikita Gushchin, Evgeny Burnaev
ICLR 2024. [Paper]

Discrete Data

Variational Flow Matching for Graph Generation Floor Eijkelboom, Grigory Bartosh, Christian Andersson Naesseth, Max Welling, Jan-Willem van de Meent
Arxiv 2024/06. [Paper]

Accelerating

Bespoke Non-Stationary Solvers for Fast Sampling of Diffusion and Flow Models Neta Shaul, Uriel Singer, Ricky T. Q. Chen, Matthew Le, Ali Thabet, Albert Pumarola, Yaron Lipman
Arxiv 2024/03. [Paper]

Applications

Flow Matching in Latent Space Quan Dao, Hao Phung, Binh Nguyen, Anh Tran
Arxiv 2023/07. [Paper]

Consistency Flow Matching: Defining Straight Flows with Velocity Consistency Ling Yang, Zixiang Zhang, Zhilong Zhang, Xingchao Liu, Minkai Xu, Wentao Zhang, Chenlin Meng, Stefano Ermon, Bin Cui
Arxiv 2024/07. [Paper]

SemFlow: Binding Semantic Segmentation and Image Synthesis via Rectified Flow Chaoyang Wang, Xiangtai Li, Lu Qi, Henghui Ding, Yunhai Tong, Ming-Hsuan Yang
Arxiv 2024/05. [Paper]

Preference Alignment with Flow Matching Minu Kim, Yongsik Lee, Sehyeok Kang, Jihwan Oh, Song Chong, Seyoung Yun
Arxiv 2024/05. [Paper]

Metric Flow Matching for Smooth Interpolations on the Data Manifold Kacper Kapusniak, Peter Potaptchik, Teodora Reu, Leo Zhang, Alexander Tong, Michael Bronstein, Avishek Joey Bose, Francesco Di Giovanni
Arxiv 2024/05. [Paper]

Lumina-T2X: Transforming Text into Any Modality, Resolution, and Duration via Flow-based Large Diffusion Transformers
Peng Gao, Le Zhuo, Ziyi Lin, Chris Liu, Junsong Chen, Ruoyi Du, Enze Xie, Xu Luo, Longtian Qiu, Yuhang Zhang, Chen Lin, Rongjie Huang, Shijie Geng, Renrui Zhang, Junlin Xi, Wenqi Shao, Zhengkai Jiang, Tianshuo Yang, Weicai Ye, He Tong, Jingwen He, Yu Qiao, Hongsheng Li
Arxiv 2024/05. [Paper]

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, Wei-Ying Ma
NeurIPS 2023. [Paper]

Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation
Ian Dunn, David Ryan Koes
Arxiv 2024/04. [Paper]

Dirichlet Flow Matching with Applications to DNA Sequence Design
Hannes Stark, Bowen Jing, Chenyu Wang, Gabriele Corso, Bonnie Berger, Regina Barzilay, Tommi Jaakkola
Arxiv 2024/02. [Paper]

D-Flow: Differentiating through Flows for Controlled Generation
Heli Ben-Hamu, Omri Puny, Itai Gat, Brian Karrer, Uriel Singer, Yaron Lipman
ICML 2024. [Paper]

Dynamic Conditional Optimal Transport through Simulation-Free Flows\ Gavin Kerrigan, Giosue Migliorini, Padhraic Smyth
Arxiv 2404. [Paper]

LayoutFlow: Flow Matching for Layout Generation
Julian Jorge Andrade Guerreiro, Naoto Inoue, Kento Masui, Mayu Otani, Hideki Nakayama
Arxiv 2403. [Paper]

Generalized Consistency Trajectory Models for Image Manipulation\ Beomsu Kim, Jaemin Kim, Jeongsol Kim, Jong Chul Ye
Arxiv 2403. [Paper]

Probabilistic Forecasting with Stochastic Interpolants and F¨ollmer Processes\ Yifan Chen, Mark Goldstein, Mengjian Hua, Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden
Arxiv 2403. [Paper]

DepthFM: Fast Monocular Depth Estimation with Flow Matching
Ming Gui, Johannes S. Fischer*, Ulrich Prestel, Pingchuan Ma, Dmytro Kotovenko, Olga Grebenkova, Stefan Andreas Baumann, Vincent Tao Hu, Björn Ommer*
Arxiv 2403. [Paper]

ZigMa: Zigzag Mamba Diffusion Model
Vincent Tao Hu, Stefan Andreas Baumann, Ming Gui, Olga Grebenkova, Pingchuan Ma, Johannes Fischer, Bjorn Ommer
ECCV 2024. [Paper]

AdaFlow: Imitation Learning with Variance-Adaptive Flow-Based Policies
Xixi Hu, Bo Liu, Xingchao Liu, Qiang Liu
Arxiv 2402. [Paper]

Precise Knowledge Transfer via Flow Matching
Shitong Shao, Zhiqiang Shen, Linrui Gong, Huanran Chen, Xu Dai
Arxiv 2402. [Paper]

Boosting Latent Diffusion with Flow Matching
Johannes S. Fischer, Ming Gui*, Pingchuan Ma*, Nick Stracke, Stefan A. Baumann, Björn Ommer*
ECCV 2024. [Paper]

Guided Flows for Generative Modeling and Decision Making
Qinqing Zheng, Matt Le, Neta Shaul, Yaron Lipman, Aditya Grover, Ricky T. Q. Chen
Arxiv 2311. [Paper]

Scaling Rectified Flow Transformers for High-Resolution Image Synthesis
Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas Müller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, Dustin Podell, Tim Dockhorn, Zion English, Kyle Lacey, Alex Goodwin, Yannik Marek, Robin Rombach
Arxiv 2403. [Paper]

Flow Matching for Conditional Text Generation in a Few Sampling Steps
Vincent Tao Hu, Di Wu, Yuki M. Asano, Pascal Mettes, Basura Fernando, Björn Ommer, Cees G.M. Snoek
EACL 2024. [Paper]

SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers
Nanye Ma, Mark Goldstein, Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden, Saining Xie
Arxiv 2401. [Paper]

AlphaFold Meets Flow Matching for Generating Protein Ensembles
Bowen Jing, Bonnie Berger, Tommi Jaakkola
Arxiv 2402. [Paper]

Bellman Optimal Step-size Straightening of Flow-Matching Models
Bao Nguyen, Binh Nguyen, Viet Anh Nguyen
Arxiv 2312. [Paper]

Latent Space Editing in Transformer-based Flow Matching
Vincent Tao Hu, David W Zhang, Pascal Mettes, Meng Tang, Deli Zhao, Cees G.M. Snoek
AAAI 2024. [Paper]

Motion Flow Matching for Human Motion Synthesis and Editing
Vincent Tao Hu, Wenzhe Yin, Pingchuan Ma, Yunlu Chen, Basura Fernando, Yuki M Asano, Efstratios Gavves, Pascal Mettes, Bjorn Ommer, Cees G. M. Snoek
Arxiv 2023. [Paper]

Guided Diffusion from Self-Supervised Diffusion Features
Vincent Tao Hu, Yunlu Chen, Mathilde Caron, Yuki M. Asano, Cees G. M. Snoek, Bjorn Ommer
Arxiv 2023. [Paper]

Mosaic-SDF for 3D Generative Models
Lior Yariv, Omri Puny, Natalia Neverova, Oran Gafni, Yaron Lipman
Arxiv 2312. [Paper]

Voicebox: Text-Guided Multilingual Universal Speech Generation at Scale
Matthew Le, Apoorv Vyas, Bowen Shi, Brian Karrer, Leda Sari, Rashel Moritz, Mary Williamson, Vimal Manohar, Yossi Adi, Jay Mahadeokar, Wei-Ning Hsu
Arxiv June 2023. [Paper]

Learn the Force We Can: Multi-Object Video Generation from Pixel-Level Interactions
Aram Davtyan, Paolo Favaro
Arxiv June 2023. [Paper]

Latent Space Editing in Transformer-based Flow Matching
Tao Hu, David W Zhang, Pascal Mettes, Meng Tang, Deli Zhao, and Cees G.M. Snoek
ICML 2023 Workshop, Oct 2023. [Paper]

Unpaired Image-to-Image Translation via Neural Schrödinger Bridge
Beomsu Kim, Gihyun Kwon, Kwanyoung Kim, Jong Chul Ye
Arxiv May 2023. [Paper]

Flow Matching for Scalable Simulation-Based Inference
Maximilian Dax, Jonas Wildberger, Simon Buchholz, Stephen R. Green, Jakob H. Macke, Bernhard Schölkopf
Arxiv May 2023. [Paper]

Equivariant flow matching
Leon Klein, Andreas Krämer, Frank Noé
Arxiv June 2023. [Paper]

Fast Point Cloud Generation with Straight Flows
Lemeng Wu, Dilin Wang, Chengyue Gong, Xingchao Liu, Yunyang Xiong, Rakesh Ranjan, Raghuraman Krishnamoorthi, Vikas Chandra, Qiang Liu
arXiv 2022. [Paper]
4 Dec 2022

Randomized Conditional Flow Matching for Video Prediction
Aram Davtyan, Sepehr Sameni, Paolo Favaro
arXiv 2022. [Paper]
16 Nov 2022

Riemannian Flow Matching on General Geometries
Ricky T. Q. Chen, Yaron Lipman
ICLR 2024. [Paper]
27 Feb 2023

Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processes
Jaehyeong Jo, Sung Ju Hwang
ICML 2024. [Paper]

Graph Generation with Diffusion Mixture
Jaehyeong Jo, Dongki Kim, Sung Ju Hwang
ICML 2024. [Paper]

InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation
Xingchao Liu, Xiwen Zhang, Jianzhu Ma, Jian Peng, qiang liu
ICLR 2024. [Paper]

Categorical Flow Matching on Statistical Manifolds
Chaoran Cheng, Jiahan Li, Jian Peng, Ge Liu
Arxiv 2024. [Paper]

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A summary of related works about flow matching, stochastic interpolants

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