Abramson, J. et al. Accurate structure prediction of biomolecular interactions with AlphaFold 3. Nature 630, 493–500 (2024).
Google Scholar
Krishna, R. et al. Generalized biomolecular modeling and design with RoseTTAFold All-Atom. Science 384, 2528 (2024).
Google Scholar
Achiam, J. et al. GPT-4 Technical Report. Preprint at https://doi.org/10.48550/arXiv.2303.08774 (2023).
Swanson, K., Wu, W., Bulaong, N. L., Pak, J. E. & Zou, J. The Virtual Lab of AI agents designs new SARS-CoV-2 nanobodies. Nature 646, 716–723 (2025).
Guo, Z. et al. Diffusion models in bioinformatics and computational biology. Nat. Rev. Bioeng. 2, 136–154 (2024).
Google Scholar
Frazer, J. et al. Disease variant prediction with deep generative models of evolutionary data. Nature 599, 91–95 (2021).
Google Scholar
Kingma, D. P. & Welling, M. Auto-encoding variational Bayes. In 2nd International Conference on Learning Representations (ICLR, 2014).
Cui, H. et al. scGPT: toward building a foundation model for single-cell multi-omics using generative AI. Nat. Methods 21, 1470–1480 (2024).
Google Scholar
Bommasani, R. et al. On the opportunities and risks of foundation models. Preprint at https://doi.org/10.48550/arXiv.2108.07258 (2021).
Anand, N. & Huang, P. Generative modeling for protein structures. In 32nd Conference on Neural Information Processing Systems (NeurIPS, 2018).
Anand, N. et al. Protein sequence design with a learned potential. Nat. Commun. 13, 746 (2022).
Google Scholar
Ho, J., Jain, A. & Abbeel, P. Denoising diffusion probabilistic models. Adv. Neural Inf. Process. Syst. 33, 6840–6851 (2020).
Hoogeboom, E., Satorras, V. G., Vignac, C. & Welling, M. Equivariant diffusion for molecule generation in 3D. Proc. Mach. Learning Res. 162, 8867–8887 (2022).
Watson, J. L. et al. De novo design of protein structure and function with RFdiffusion. Nature 620, 1089–1100 (2023).
Google Scholar
Shome, D., Sarkar, P. & Etemad, A. Region-disentangled diffusion model for high-fidelity PPG-to-ECG translation. In Proc. AAAI Conference on Artificial Intelligence Vol. 38, 15009–15019 (AAAI Press, 2024).
Miller, B. K., Chen, R. T. Q., Sriram, A. & Wood, B. M. FlowMM: generating materials with Riemannian Flow Matching. In Proc. 41st International Conference on Machine Learning Vol. 235, 35664–35686 (JMLR.org, 2024).
LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015).
Google Scholar
Lipman, Y., Chen, R. T., Ben-Hamu, H., Nickel, M. & Le, M. Flow matching for generative modeling. In 11th International Conference on Learning Representations (ICLR, 2023).
Bunne, C. et al. How to build the virtual cell with artificial intelligence: priorities and opportunities. Cell 187, 7045–7063 (2024).
Google Scholar
Lipman, Y. et al. Flow matching guide and code. NeurIPS Tutorial https://neurips.cc/virtual/2024/tutorial/99531 (2024).
Tabak, E. G. & Vanden-Eijnden, E. Density estimation by dual ascent of the log-likelihood. Commun. Math. Sci. 8, 217–233 (2010).
Google Scholar
Tabak, E. G. & Turner, C. V. A family of nonparametric density estimation algorithms. Commun. Pure Appl. Math. 66, 145–164 (2013).
Google Scholar
Rezende, D. & Mohamed, S. Variational inference with normalizing flows. Proc. Mach. Learning Res. 37, 1530–1538 (2015).
Peluchetti, S. Non-denoising forward-time diffusions. Preprint at https://doi.org/10.48550/arXiv.2312.14589 (2023).
Yang, L. et al. Diffusion models: a comprehensive survey of methods and applications. ACM Comput. Surv. 56, 1–39 (2023).
Google Scholar
Tong, A. et al. Improving and generalizing flow-based generative models with minibatch optimal transport. In Transactions on Machine Learning Research (TMLR, 2024). This article introduces a generally tractable training objective for FM in generative AI.
Chen, R. T. Q. & Lipman, Y. Flow matching on general geometries. In 12th International Conference on Learning Representations (ICLR, 2024).
Kornilov, N., Mokrov, P., Gasnikov, A. & Korotin, A. Optimal Flow Matching: learning straight trajectories in just one step. Adv. Neural Inf. Process. Syst. 37, 104180–104204 (2024).
Chen, R. T., Rubanova, Y., Bettencourt, J. & Duvenaud, D. K. Neural ordinary differential equations. In 32nd Conference on Neural Information Processing Systems (NeurIPS, 2018). This article introduces the theoretical foundations necessary for generative FM of differential systems.
Chen, R. T., Behrmann, J., Duvenaud, D. K. & Jacobsen, J.-H. Residual flows for invertible generative modeling. In 33rd Conference on Neural Information Processing Systems (NeurIPS, 2019).
Hoffman, M. D., Blei, D. M., Wang, C. & Paisley, J. Stochastic variational inference. J. Mach. Learning Res. 14, 1303–1347 (2013).
Bose, J. et al. SE(3)-stochastic flow matching for protein backbone generation. In 12th International Conference on Learning Representations (ICLR, 2024).
Yim, J. et al. Fast protein backbone generation with SE(3) flow matching. In NeurIPS Machine Learning in Structural Biology Workshop (2023).
Atanackovic, L. et al. Meta Flow Matching: integrating vector fields on the Wasserstein manifold. In 13th International Conference on Learning Representations (ICLR, 2024).
Haviv, D., Pooladian, A.-A., Pe’er, D. & Amos, B. Wasserstein flow matching: generative modeling over families of distributions. In Proc. 42nd International Conference on Machine Learning (JMLR.org, 2025).
Qiao, Z. et al. NeuralPLexer3: accurate biomolecular complex structure prediction with flow models. In 39th Conf. Neural Information Processing Systems (NeurIPS, 2025).
Zhang, Y. et al. CellFlux: simulating cellular morphology changes via flow matching. In Proc. 42nd International Conference on Machine Learning (JMLR.org, 2025).
Iserles, A. A First Course in the Numerical Analysis of Differential Equations (Cambridge Univ. Press, 2009).
Gat, I. et al. Discrete Flow Matching. Adv. Neural Inf. Process. Syst. 37, 133345–133385 (2024).
Dunn, I. & Koes, D. R. Exploring discrete flow matching for 3D de novo molecule generation. In NeurIPS Machine Learning in Structural Biology Workshop (NeurIPS, 2024).
Stark, H., Jing, B., Barzilay, R. & Jaakkola, T. Harmonic self-conditioned flow matching for joint multi-ligand docking and binding site design. In Proc. 41st International Conference on Machine Learning (JMLR.org, 2024).
Campbell, A., Yim, J., Barzilay, R., Rainforth, T. & Jaakkola, T. Generative flows on discrete state-spaces: enabling multimodal flows with applications to protein co-design. In International Conference on Machine Learning Vol. 235, 5453–5512 (JMLR, 2024).
Peng, F. Z. et al. Planner aware path learning in diffusion language models training. In 15th International Conference on Learning Representations (ICLR, 2026).
Huguet, G. et al. Sequence-augmented SE (3)-flow matching for conditional protein generation. Adv. Neural Inf. Process. Syst. 37, 33007–33036 (2024).
Yim, J. et al. SE(3) diffusion model with application to protein backbone generation. In Proc. 40th International Conference on Machine Learning Vol. 202, 40001–40039 (JMLR.org, 2023).
Lee, J. S. & Kim, P. M. FlowPacker: protein side-chain packing with torsional flow matching. Bioinformatics 41, 010 (2025).
Google Scholar
Joshi, C. K. et al. All-atom diffusion transformers: unified generative modelling of molecules and materials. In Proc. 42nd International Conference on Machine Learning Vol. 267, 28393–28417 (PMLR, 2025).
Yim, J. et al. Diffusion models in protein structure and docking. Wiley Interdiscip. Rev. Comput. Mol. Sci. 14, 1711 (2024).
Google Scholar
Albergo, M. S. & Vanden-Eijnden, E. Building normalizing flows with stochastic interpolants. In 11th International Conference on Learning Representations (ICLR, 2023).
Liu, X. et al. Flow straight and fast: learning to generate and transfer data with rectified flow. In 11th International Conference on Learning Representations (ICLR, 2023).
Geng, Z., Deng, M., Bai, X., Kolter, J. Z. & He, K. Mean flows for one-step generative modeling. In 39th Conf. Neural Information Processing Systems (NeurIPS, 2025).
Holderrieth, P. et al. Generator Matching: generative modeling with arbitrary Markov processes. In 13th International Conference on Learning Representations (ICLR, 2025).
Vaswani, A. et al. Attention is all you need. In Proc. 31st International Conference on Neural Information Processing Systems 6000–6010 (2017).
Wu, K., Karapetyan, E., Schloss, J., Vadgama, J. & Wu, Y. Advancements in small molecule drug design: a structural perspective. Drug Discov. Today 28, 103730 (2023).
Google Scholar
Irwin, R., Tibo, A., Janet, J. P. & Olsson, S. SemlaFlow—efficient 3D molecular generation with latent attention and equivariant flow matching. The 28th International Conference on Artificial Intelligence and Statistics (2025).
Dunn, I. & Koes, D. R. Mixed continuous and categorical flow matching for 3D de novo molecule generation. Preprint at https://doi.org/10.48550/arXiv.2404.19739 (2024).
Jing, B., Eismann, S., Suriana, P., Townshend, R. J. L. & Dror, R. Learning from protein structure with geometric vector perceptrons. In 9th International Conference on Learning Representations (ICLR, 2021).
Hassan, M. et al. ET-Flow: equivariant flow-matching for molecular conformer generation. Adv. Neural Inf. Process. Syst. 37, 128798–128824 (2024).
Huang, P.-S., Boyken, S. E. & Baker, D. The coming of age of de novo protein design. Nature 537, 320–327 (2016).
Google Scholar
Yan, J. et al. Robust and reliable de novo protein design: a flow-matching-based protein generative model achieves remarkably high success rates. Preprint at bioRxiv https://doi.org/10.1101/2025.04.29.651154 (2025).
Barrangou, R. & Doudna, J. A. Applications of CRISPR technologies in research and beyond. Nat. Biotechnol. 34, 933–941 (2016).
Google Scholar
Stark, H. et al. Dirichlet flow matching with applications to DNA sequence design. Proc. Mach. Learning Res. 235, 46495–46513 (2024).
Davis, O. et al. Fisher flow matching for generative modeling over discrete data. Adv. Neural Inf. Process. Syst. 37, 139054–139084 (2024).
Gao, L. & Lu, Z. J. RNACG: a universal RNA sequence conditional generation model based on flow-matching. Preprint at https://doi.org/10.48550/arXiv.2407.19838 (2024).
Nori, D. & Jin, W. RNAFlow: RNA structure & sequence design via inverse folding-based flow matching. In Proc. 41st International Conference on Machine Learning 38395–38408 (JMLR.org, 2024).
Ma, R. et al. RiboFlow: conditional de novo RNA sequence–structure co-design via synergistic flow matching. In 39th Conference on Neural Information Processing Systems (NeurIPS, 2025).
Abir, A. R. & Zhang, L. RNA-EFM: energy-based flow matching for protein-conditioned RNA sequence–structure co-design. Bioinform. Adv. 5, vbaf258 (2025).
Anand, R. et al. RNA-FrameFlow: flow matching for de novo 3D RNA backbone design. In Transactions on Machine Learning Research (TMLR, 2025).
Tarafder, S. & Bhattacharya, D. RNAbpFlow: base pair-augmented SE (3)-flow matching for conditional RNA 3D structure generation. Preprint at bioRxiv https://doi.org/10.1101/2025.01.24.634669 (2025).
Morehead, A., Giri, N., Liu, J. & Cheng, J. Deep learning for protein–ligand docking: are we there yet? In ICML AI for Science Workshop (ICML, 2024).
Morehead, A. & Cheng, J. FlowDock: geometric flow matching for generative protein–ligand docking and affinity prediction. Bioinformatics 41, i198–i206 (2025).
Corso, G. et al. Composing unbalanced flows for flexible docking and relaxation. In 13th International Conference on Learning Representations (ICLR, 2025).
Kong, X. et al. UniMoMo: unified generative modeling of 3D molecules for de novo binder design. In Proc. 42nd International Conference on Machine Learning (JMLR.org, 2025).
Mortier, J. et al. The impact of molecular dynamics on drug design: applications for the characterization of ligand–macromolecule complexes. Drug Discov. Today 20, 686–702 (2015).
Google Scholar
Jing, B., Berger, B. & Jaakkola, T. AlphaFold meets flow matching for generating protein ensembles. In Proc. 41st International Conference on Machine Learning (JMLR.org, 2024).
Zhang, M., Zhang, Z., Wu, H. & Wang, Y. Flow matching for optimal reaction coordinates of biomolecular systems. J. Chem. Theory Comput. 21, 399–412 (2024).
Google Scholar
Jing, B., Stärk, H., Jaakkola, T. & Berger, B. Generative modeling of molecular dynamics trajectories. Adv. Neural Inf. Process. Syst. 37, 40534–40564 (2024).
Raja, S. et al. Action-minimization meets generative modeling: efficient transition path sampling with the Onsager–Machlup functional. In Proc. 42nd International Conference on Machine Learning (JMLR.org, 2025).
Yofe, I., Dahan, R. & Amit, I. Single-cell genomic approaches for developing the next generation of immunotherapies. Nat. Med. 26, 171–177 (2020).
Google Scholar
Klein, D. et al. CellFlow enables generative single-cell phenotype modeling with flow matching. Preprint at bioRxiv https://doi.org/10.1101/2025.04.11.648220 (2025).
Palma, A. et al. Multi-modal and multi-attribute generation of single cells with CFGen. In 13th International Conference on Learning Representations (ICLR, 2025).
Tong, A. et al. Simulation-free Schrödinger bridges via score and flow matching. Proc. Mach. Learning Res. 238, 1279–1287 (2024).
Klein, D., Uscidda, T., Theis, F. & Cuturi, M. GENOT: entropic (Gromov) Wasserstein flow matching with applications to single-cell genomics. Adv. Neural Inf. Process. Syst. 37, 103897–103944 (2024).
Kapusniak, K. et al. Metric Flow Matching for smooth interpolations on the data manifold. Adv. Neural Inf. Process. Syst. 37, 135011–135042 (2024).
Zhang, Z., Wang, Z., Sun, Y., Li, T. & Zhou, P. Modeling cell dynamics and interactions with Unbalanced Mean Field Schrödinger Bridge. In 39th Conf. Neural Information Processing Systems (NeurIPS, 2025).
Petrović, K. et al. Curly flow matching for learning non-gradient field dynamics. In 39th Conf. Neural Information Processing Systems (NeurIPS, 2025).
Wang, D. et al. Joint velocity–growth flow matching for single-cell dynamics modeling. In 39th Conf. Neural Information Processing Systems (NeurIPS, 2025).
Rohbeck, M. et al. Modeling complex system dynamics with flow matching across time and conditions. In 13th International Conference on Learning Representations (ICLR, 2025).
Kim, S.-J., Kim, E. M., Yamamoto, M., Park, H. & Shin, H. Engineering multi-cellular spheroids for tissue engineering and regenerative medicine. Adv. Healthc. Mater. 9, 2000608 (2020).
Google Scholar
Bourou, A. et al. PhenDiff: revealing subtle phenotypes with diffusion models in real images. In Medical Image Computing and Computer Assisted Intervention—MICCAI 2024 Lecture Notes in Computer Science Vol. 15003 (eds Linguraru, M. G. et al.) 358–367 (Springer, 2024).
Palma, A., Theis, F. J. & Lotfollahi, M. Predicting cell morphological responses to perturbations using generative modeling. Nat. Commun. 16, 505 (2025).
Google Scholar
Weissleder, R. & Nahrendorf, M. Advancing biomedical imaging. Proc. Natl Acad. Sci. USA 112, 14424–14428 (2015).
Google Scholar
Zhou, Y., Li, Y., Yuan, J. & Gu, Q. CryoFM: a flow-based foundation model for cryo-EM densities. In 13th International Conference on Learning Representations (ICLR, 2025).
Bogensperger, L., Narnhofer, D., Falk, A., Schindler, K. & Pock, T. FlowSDF: flow matching for medical image segmentation using distance transforms. Int. J. Comput. Vision 133, 4864–4876 (2025).
Google Scholar
Kumar, N. et al. A dataset and a technique for generalized nuclear segmentation for computational pathology. IEEE Trans. Med. Imaging 36, 1550–1560 (2017).
Google Scholar
Sirinukunwattana, K. et al. Gland segmentation in colon histology images: the GlaS Challenge Contest. Med. Image Anal. 35, 489–502 (2017).
Google Scholar
Luo, X., Li, Y. & Qin, C. Unsupervised accelerated MRI reconstruction via ground-truth-free flow matching. In Information Processing in Medical Imaging. IPMI 2025 Lecture Notes in Computer Science Vol. 15829 (eds Oguz, I. et al.) 127–141 (Springer, 2025).
Zhang, D., Han, Q., Xiong, Y. & Du, H. Multi-modal straight flow matching for accelerated MR imaging. Comput. Biol. Med. 178, 108668 (2024).
Google Scholar
Yazdani, M., Medghalchi, Y., Ashrafian, P., Hacihaliloglu, I. & Shahriari, D. Flow matching for medical image synthesis: bridging the gap between speed and quality. In Medical Image Computing and Computer Assisted Intervention. MICCAI 2025. Lecture Notes in Computer Science Vol. 15975, 216–226 (Springer, 2025).
Qu, E. & Krishnapriyan, A. The importance of being scalable: improving the speed and accuracy of neural network interatomic potentials across chemical domains. Adv. Neural Inf. Process. Syst. 37, 139030–139053 (2024).
Doudna, J. A. & Charpentier, E. The new frontier of genome engineering with CRISPR-Cas9. Science 346, 1258096 (2014).
Google Scholar
Paszke, A. PyTorch: an imperative style, high-performance deep learning library. In Proc. 33rd International Conference on Neural Information Processing Systems 8026–8037 (ACM, 2019).
Lim, S. H. et al. Elucidating the design choice of probability paths in flow matching for forecasting. In Transactions on Machine Learning Research (TMLR, 2025).
Kruiff, F., Bekkers, E., Öktem, O., Schönlieb, C.-B. & Diepeveen, W. Pullback flow matching on data manifolds. In ICML Generative AI and Biology Workshop (ICML, 2025).
Klein, L., Krämer, A. & Noé, F. Equivariant flow matching. Adv. Neural Inf. Process. Syst. 36, 59886–59910 (2023).
Google Scholar
Zhu, H., Wang, F., Ding, T., Qu, Q. & Zhu, Z. Analyzing and improving model collapse in rectified flow models. Preprint at https://doi.org/10.48550/arXiv.2412.08175 (2024).
Zhang, H. et al. AlphaFlow: understanding and improving MeanFlow models. Preprint at https://doi.org/10.48550/arXiv.2510.20771 (2025).
Reu, T., Dromigny, S., Bronstein, M. M. & Vargas, F. Flows don’t cross in high dimension. In ICLR Workshop on Deep Generative Model in Machine Learning: Theory, Principle and Efficacy (ICLR, 2025).
Dhariwal, P. & Nichol, A. Diffusion models beat GANs on image synthesis. Adv. Neural Inf. Process. Syst. 34, 8780–8794 (2021).
Yacoby, Y., Pan, W. & Doshi-Velez, F. Failure modes of variational autoencoders and their effects on downstream tasks. Preprint at https://doi.org/10.48550/arXiv.2007.07124 (2020).
Huang, C.-W., Krueger, D., Lacoste, A. & Courville, A. Neural autoregressive flows. Proc. Mach. Learning Res. 80, 2078–2087 (2018).
Kingma, D. P. & Dhariwal, P. Glow: generative flow with invertible 1×1 convolutions. In Proc. 32nd International Conference on Neural Information Processing Systems 10236–10245 (NIPS, 2018).
Grathwohl, W., Chen, R.T., Bettencourt, J., Sutskever, I. & Duvenaud, D. FFJORD: free-form continuous dynamics for scalable reversible generative models. In 7th International Conference on Learning Representations (ICLR, 2019).
Dupont, E., Doucet, A. & Teh, Y. W. Augmented neural ODEs. Adv. Neural Inf. Process. Syst. 32, (2019).
Liu, J., Kumar, A., Ba, J., Kiros, J. & Swersky, K. Graph normalizing flows. Adv. Neural Inf. Process. Syst. 32 (2019).
Wu, H., Köhler, J. & Noé, F. Stochastic Normalizing Flows. Adv. Neural Inf. Process. Syst. 33, 5933–5944 (2020).
Hodgkinson, L., Heide, C., Roosta, F. & Mahoney, M. W. Stochastic continuous normalizing flows: training SDEs as ODEs. Proc. Mach. Learning Res. 161, 1130–1140 (2021).
Garcia Satorras, V., Hoogeboom, E., Fuchs, F., Posner, I. & Welling, M. E(n) equivariant normalizing flows. Adv. Neural Inf. Process. Syst. 34, 4181–4192 (2021).
Zhang, Q. & Chen, Y. Diffusion normalizing flow. Adv. Neural Inf. Process. Syst. 34, 16280–16291 (2021).
Gabrié, M., Rotskoff, G. M. & Vanden-Eijnden, E. Adaptive Monte Carlo augmented with normalizing flows. Proc. Natl Acad. Sci. USA 119, 2109420119 (2022).
Google Scholar
Richter-Powell, J., Lipman, Y. & Chen, R. T. Neural conservation laws: a divergence-free perspective. Adv. Neural Inf. Process. Syst. 35, 38075–38088 (2022).
Albergo, M. S., Boffi, N. M. & Vanden-Eijnden, E. Stochastic interpolants: a unifying framework for flows and diffusions. J. Mach. Learn. Res. 26, 1–80 (2025).
Albergo, M. S., Goldstein, M., Boffi, N. M., Ranganath, R. & Vanden-Eijnden, E. Stochastic interpolants with data-dependent couplings. Proc. Mach. Learning Res. 235, 921–937 (2024).
Davtyan, A., Sameni, S. & Favaro, P. Efficient video prediction via sparsely conditioned flow matching. In IEEE/CVF International Conference on Computer Vision 23263–23274 (IEEE, 2023).
Wu, L. et al. Fast point cloud generation with straight flows. In IEEE/CVF Conference on Computer Vision and Pattern Recognition 9445–9454 (IEEE, 2023).
Neklyudov, K., Brekelmans, R., Severo, D. & Makhzani, A. Action Matching: learning stochastic dynamics from samples. In Proc. 40th International Conference on Machine Learning Vol. 202 (ed. Krause, A.) 25858–25889 (JMLR.org, 2023).
Lee, S., Kim, B. & Ye, J.C. Minimizing trajectory curvature of ODE-based generative models. Proc. Mach. Learning Res. 202, 18957–18973 (2023).
Dao, Q., Phung, H., Nguyen, B. & Tran, A. Flow matching in latent space. Preprint at https://doi.org/10.48550/arXiv.2307.08698 (2023).
Neklyudov, K. et al. A computational framework for solving Wasserstein Lagrangian flows. In Proc. 41st International Conference on Machine Learning (JMLR.org, 2024).
Schusterbauer, J. et al FMBoost: boosting latent diffusion with flow matching. In Computer Vision ECCV 2024. Lecture Notes in Computer Science (eds Leonardis, A. et al.) Vol. 15119, 338–355 (Springer, 2025).
Hu, V. T. et al. Motion Flow Matching for human motion synthesis and editing. Preprint at https://doi.org/10.48550/arXiv.2312.08895 (2023).
Liu, X. et al. InstaFlow: one step is enough for high-quality diffusion-based text-to-image generation. In 12th International Conference on Learning Representations (ICLR, 2023).
Kerrigan, G., Migliorini, G. & Smyth, P. Functional Flow Matching. Proc. Mach. Learning Res. 238, 3934–3942 (2024).
Nguyen, B., Nguyen, B. & Nguyen, V. A. Bellman optimal stepsize straightening of flow-matching models. In 13th International Conference on Learning Representations (ICLR, 2024).
Yang, L. et al. Consistency Flow Matching: defining straight flows with velocity consistency. Preprint at https://doi.org/10.48550/arXiv.2407.02398 (2024).
Gui, M. et al. DepthFM: fast generative monocular depth estimation with flow matching. In Proc. AAAI Conference on Artificial Intelligence Vol. 39 No. 3: AAAI-25 Technical Tracks 3 (eds Walsh, T. et al.) 3203–3211 (AAAI Press, 2025).
Chen, Y. et al. Probabilistic forecasting with stochastic interpolants and Föllmer processes. Proc. Mach. Learning Res. 235, 6728–6756 (2024).
Wang, C. et al. SemFlow: binding semantic segmentation and image synthesis via rectified flow. Adv. Neural Inf. Process. Syst. 37, 138981–139001 (2024).
Kim, M. et al. Preference alignment with flow matching. Adv. Neural Inf. Process. Syst. 37, 35140–35164 (2024).
Kerrigan, G., Migliorini, G. & Smyth, P. Dynamic conditional optimal transport through simulation-free flows. Adv. Neural Inf. Process. Syst. 37, 93602–93642 (2024).
Google Scholar
Hu, V. et al. Flow matching for conditional text generation in a few sampling steps. In Proc. 18th Conference of the European Chapter of the Association for Computational Linguistics Vol. 2: Short Papers (eds Graham, Y. & Purver, M.) 380–392 (ACL, 2024).
Cheng, C., Li, J., Peng, J. & Liu, G. Categorical flow matching on statistical manifolds. Adv. Neural Inf. Process. Syst. 37, 54787–54819 (2024).
Google Scholar
Nisonoff, H., Xiong, J., Allenspach, S. & Listgarten, J. Unlocking guidance for discrete state-space diffusion and flow models. In 13th International Conference on Learning Representations (ICLR, 2025).
Zhang, X. N. et al. Trajectory Flow Matching with applications to clinical time series modelling. Adv. Neural Inf. Process. Syst. 37, 107198–107224 (2024).
Stoica, G. et al. Contrastive Flow Matching. In IEEE/CVF International Conference on Computer Vision 1185–1194 (IEEE, 2025).
Lin, H. et al. TFG-Flow: training-free guidance in multimodal generative flow. In 13th International Conference on Learning Representations (ICLR, 2025).
Bartosh, G., Vetrov, D. & Naesseth, C. A. SDE Matching: scalable and simulation-free training of latent stochastic differential equations. In Proc. 42nd International Conference on Machine Learning (JMLR.org, 2025).
Song, Y. et al. Equivariant flow matching with hybrid probability transport for 3D molecule generation. Adv. Neural Inf. Process. Syst. 36, 549–568 (2023).
Kong, Z. et al. ProtFlow: fast protein sequence design via flow matching on compressed protein language model embeddings. Preprint at https://doi.org/10.48550/arXiv.2504.10983 (2025).
Yang, S. et al. Co-design protein sequence and structure in discrete space via generative flow. Bioinformatics 41, btaf248 (2025).
Google Scholar
Wu, J. et al. FlowDesign: improved design of antibody CDRs through flow matching and better prior distributions. Cell Syst. 16, 101270 (2025).
Google Scholar
Wu, F. et al. D-Flow: multi-modality flow matching for D-peptide design. In NeurIPS Workshop on AI Virtual Cells and Instruments (NeurIPS, 2025).
Li, J. et al. Full-atom peptide design based on multi-modal flow matching. Proc. Mach. Learning Res. 235, 27615–27640 (2024).
Lin, H. et al. PPFlow: target-aware peptide design with torsional flow matching. Proc. Mach. Learning Res. 235, 30510–30528 (2024).
Yu, Z., Huang, W. & Liu, Y. UniSim: a unified simulator for time-coarsened dynamics of biomolecules. In Proc. 42nd International Conference on Machine Learning (JMLR.org, 2025).
Hurst, A. et al. GPT-4o system card. Preprint at https://doi.org/10.48550/arXiv.2410.21276 (2024).
Esser, P. et al. Scaling rectified flow transformers for high-resolution image synthesis. In Proc. 41st International Conference on Machine Learning (JMLR.org, 2024).
Salakhutdinov, R. Learning deep generative models. Annu. Rev. Stat. Appl. 2, 361–385 (2015).
Google Scholar
Peyré, G. et al. Computational optimal transport: with applications to data science. Found. Trends Mach. Learning 11, 355–607 (2019).
Google Scholar
Corso, G. et al. Graph neural networks. Nat. Rev. Methods Primers 4, 17 (2024).
Google Scholar
Geiger, M. & Smidt, T. e3nn: Euclidean neural networks. Preprint at https://doi.org/10.48550/arXiv.2207.09453 (2022).
Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R. & Mahoney, M. W. Characterizing possible failure modes in physics-informed neural networks. Adv. Neural Inf. Process. Syst. 34, 26548–26560 (2021).
