Generative Models for Decision Making Under Distributional Shift

References

• [1] M. S. Albergo and E. Vanden-Eijnden. Building normalizing flows with stochastic interpolants. Proceedings of the International Conference on Learning Representations, 2023.Google Scholar
• [2] M. S. Albergo, N. M. Boffi, and E. Vanden-Eijnden. Stochastic interpolants: A unifying framework for flows and diffusions. Journal of Machine Learning Research 1–80, 2025.Google Scholar
• [3] S. Amari. Information geometry and its applications: Convex function and dually flat manifold. Proceedings of the VIX Fall Colloquium on Emerging Trends in Visual Computing. Springer, Berlin, 75–102, 2008.Google Scholar
• [4] S. Amari. Information Geometry and Its Applications, vol. 194. Springer, Berlin, 2016.Crossref, Google Scholar
• [5] L. Ambrosio, N. Gigli, and G. Savaré. Gradient Flows: In Metric Spaces and in the Space of Probability Measures. Springer Science & Business Media, Boston, 2005.Google Scholar
• [6] L. Ardizzone, J. Kruse, S. Wirkert, D. Rahner, E. W. Pellegrini, R. S. Klessen, L. Maier-Hein, et al. Analyzing inverse problems with invertible neural networks. Proceedings of the International Conference on Learning Representations, 2019.Google Scholar
• [7] J. Behrmann, W. Grathwohl, R. T. Chen, D. Duvenaud, and J. H. Jacobsen. Invertible residual networks. Proceedings of the International Conference on Machine Learning, 573–582, 2019.Google Scholar
• [8] J. D. Benamou and Y. Brenier. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numerische Mathematik 84(3):375–393, 2000.Crossref, Google Scholar
• [9] J. Blanchet and K. Murthy. Quantifying distributional model risk via optimal transport. Mathematics of Operations Research 44(2):565–600, 2019.Link, Google Scholar
• [10] R. Carmona and F. Delarue. Probabilistic Theory of Mean Field Games with Applications I-II, volume 3. Springer, Berlin, 2018.Crossref, Google Scholar
• [11] R. T. Chen, Y. Rubanova, J. Bettencourt, and D. K. Duvenaud. Neural ordinary differential equations. Proceedings of the Conference on Neural Information Processing Systems, volume 31, 2018.Google Scholar
• [12] X. Cheng, J. Lu, Y. Tan, and Y. Xie. Convergence of flow-based generative models via proximal gradient descent in Wasserstein space. IEEE Transactions on Information Theory 11:8087–8106, 2024.Crossref, Google Scholar
• [13] X. Cheng, Y. Xie, L. Zhu, and Y. Zhu. Worst-case generation via minimax optimization in wasserstein space. Preprint, submitted December 9, https://arxiv.org/abs/2512.08176, 2025.Google Scholar
• [14] H. Chung, J. Kim, M. T. McCann, M. L. Klasky, and J. C. Ye. Diffusion posterior sampling for general noisy inverse problems. Proceedings of the International Conference on Learning Representations, 2023.Google Scholar
• [15] N. Courty, R. Flamary, and D. Tuia. Domain adaptation with regularized optimal transport. Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases. Springer, 274–289, 2014.Google Scholar
• [16] N. Courty, R. Flamary, A. Habrard, and A. Rakotomamonjy. Joint distribution optimal transportation for domain adaptation. Proceedings of the Conference on Advances in Neural Information Processing Systems, volume 30, 2017.Google Scholar
• [17] L. Dinh, D. Krueger, and Y. Bengio. NICE: Non-linear independent components estimation. Proceedings of the International Conference on Learning Representations, 2015.Google Scholar
• [18] L. Dinh, J. Sohl-Dickstein, and S. Bengio. Density estimation using Real NVP. Proceedings of the International Conference on Learning Representations, 2017.Google Scholar
• [19] J. Fan, Q. Zhang, A. Taghvaei, and Y. Chen. Variational Wasserstein gradient flow. Proceedings of the International Conference on Machine Learning, 6185–6215, 2022.Google Scholar
• [20] R. Gao and A. Kleywegt. Distributionally robust stochastic optimization with Wasserstein distance. Mathematics of Operations Research 48(2):603–655, 2023.Link, Google Scholar
• [21] A. P. Generale, A. Robertson, and S. Kalidindi. Conditional variable flow matching: Transforming conditional densities with amortized conditional optimal transport. Preprint, submitted November 13, https://arxiv.org/abs/2411.08314, 2024.Google Scholar
• [22] I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. C. Courville, et al. Generative adversarial nets. Proceedings of the Conference on Neural Information Processing Systems, 2014.Google Scholar
• [23] W. Grathwohl, R. T. Chen, J. Bettencourt, I. Sutskever, and D. Duvenaud. FFJORD: Free-form continuous dynamics for scalable reversible generative models. Proceedings of the International Conference on Learning Representations, 2018.Google Scholar
• [24] I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A. C. Courville. Improved training of Wasserstein GANs. Proceedings of the Conference on Neural Information Processing Systems, 2017.Google Scholar
• [25] K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 770–778, 2016.Google Scholar
• [26] J. Ho and T. Salimans. Classifier-free diffusion guidance. Proceedings of the Conference on Neural Information Processing Systems Workshop on Deep Generative Models and Downstream Applications, 2021.Google Scholar
• [27] J. Ho, A. Jain, and P. Abbeel. Denoising diffusion probabilistic models. Proceedings of the Conference on Advances in Neural Information Processing Systems, volume 33, 6840–6851, 2020.Google Scholar
• [28] M. Huang, R. P. Malhamé, and P. E. Caines. Large population stochastic dynamic games: Closed-loop Mckean-Vlasov systems and the nash certainty equivalence principle. Communications in Information and Systems 6(3):221–252, 2006.Crossref, Google Scholar
• [29] A. Hyvärinen and P. Dayan. Estimation of non-normalized statistical models by score matching. Journal of Machine Learning Research 6(4):695–709, 2005.Google Scholar
• [30] P. Isola, J. Y. Zhu, T. Zhou, and A. A. Efros. Image-to-image translation with conditional adversarial networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 5967–5976, 2017.Google Scholar
• [31] R. Jordan, D. Kinderlehrer, and F. Otto. The variational formulation of the Fokker–Planck equation. SIAM Journal on Mathematical Analysis 29(1):1–17, 1998.Crossref, Google Scholar
• [32] C. Kent, J. Li, J. Blanchet, and P. W. Glynn. Modified Frank Wolfe in probability space. Advances in Neural Information Processing Systems 34:14448–14462, 2021.Google Scholar
• [33] D. P. Kingma and P. Dhariwal. Glow: Generative flow with invertible 1x1 convolutions. Proceedings of the Advances in Neural Information Processing Systems, volume 31, 2018.Google Scholar
• [34] D. P. Kingma and M. Welling. Auto-encoding variational Bayes. Proceedings of the International Conference on Learning Representations, 2014.Google Scholar
• [35] D. P. Kingma and M. Welling. An introduction to variational autoencoders. Foundations and Trends® in Machine Learning 12(4):307–392, 2019.Crossref, Google Scholar
• [36] I. Kobyzev, S. J. Prince, and M. A. Brubaker. Normalizing flows: An introduction and review of current methods. IEEE Transactions on Pattern Analysis and Machine Intelligence 43(11):3964–3979, 2020.Crossref, Google Scholar
• [37] D. Kuhn, P. M. Esfahani, V. A. Nguyen, and S. Shafieezadeh-Abadeh. Wasserstein distributionally robust optimization: Theory and applications in machine learning. TutORials in Operations Research. INFORMS, 130–166, 2019.Link, Google Scholar
• [38] J. M. Lasry and P. L. Lions. Mean field games. Japanese Journal of Mathematics 2(1):229–260, 2007.Crossref, Google Scholar
• [39] T. Lin, C. Jin, and M. Jordan. On gradient descent ascent for nonconvex-concave minimax problems. Proceedings of the International Conference on Machine Learning, 6083–6093, 2020.Google Scholar
• [40] Y. Lipman, R. T. Q. Chen, H. Ben-Hamu, M. Nickel, and M. Le. Flow matching for generative modeling. Proceedings of the International Conference on Learning Representations, 2023.Google Scholar
• [41] Y. Lipman, M. Havasi, P. Holderrieth, N. Shaul, M. Le, B. Karrer, R. T. Chen, et al. Flow matching guide and code. Preprint, submitted December 9, https://arxiv.org/abs/2412.06264, 2024.Google Scholar
• [42] Q. Liu. Rectified flow: A marginal preserving approach to optimal transport. Preprint, submitted September 29, https://arxiv.org/abs/2209.14577, 2022.Google Scholar
• [43] A. Liutkus, U. Simsekli, S. Majewski, A. Durmus, and F. R. Stöter. Sliced-Wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions. Proceedings of the International Conference on Machine Learning, 4104–4113, 2019.Google Scholar
• [44] A. Makkuva, A. Taghvaei, S. Oh, and J. Lee. Optimal transport mapping via input convex neural networks. Proceedings of the International Conference on Machine Learning. PMLR, 6672–6681, 2020.Google Scholar
• [45] M. Min and R. Hu. Signatured deep fictitious play for mean field games with common noise. Proceedings of the International Conference on Machine Learning, 2021.Google Scholar
• [46] P. Mohajerin Esfahani and D. Kuhn. Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Mathematical Programming 171(1):115–166, 2018.Crossref, Google Scholar
• [47] P. Mokrov, A. Korotin, L. Li, A. Genevay, J. M. Solomon, and E. Burnaev. Large-scale Wasserstein gradient flows. Conference on Neural Information Processing Systems (NeurIPS) 34:15243–15256, 2021. Google Scholar
• [48] D. Onken, S. Wu Fung, X. Li, and L. Ruthotto. OT-flow: Fast and accurate continuous normalizing flows via optimal transport. Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, 2021.Google Scholar
• [49] V. Purohit, M. Repasky, J. Lu, Q. Qiu, Y. Xie, and X. Cheng. Posterior sampling via langevin dynamics based on generative priors. Proceedings of the Conference on Computer Vision and Pattern Recognition, 2024.Google Scholar
• [50] L. Ruthotto, S. J. Osher, W. Li, L. Nurbekyan, and S. W. Fung. A machine learning framework for solving high-dimensional mean field game and mean field control problems. Proceedings of the National Academy of Sciences United States of America 117(17):9183–9193, 2020.Crossref, Google Scholar
• [51] C. Silvia, J. Ray, S. Tom, P. Aldo, J. Heinrich, and A. John. A general approach to fairness with optimal transport. Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, 3633–3640, 2020.Google Scholar
• [52] A. Sinha, H. Namkoong, R. Volpi, and J. Duchi. Certifying some distributional robustness with principled adversarial training. Proceedings of the International Conference on Learning Representations, 2018.Google Scholar
• [53] Y. Song and S. Ermon. Generative modeling by estimating gradients of the data distribution. Proceedings of the Advances in Neural Information Processing Systems, volume 32, 2019.Google Scholar
• [54] J. Song, C. Meng, and S. Ermon. Denoising diffusion implicit models. Proceedings of the International Conference on Learning Representations, 2021.Google Scholar
• [55] Y. Song, P. Dhariwal, M. Chen, and I. Sutskever. Consistency models. Proceedings of the International Conference on Machine Learning, 2023.Google Scholar
• [56] Y. Song, L. Shen, L. Xing, and S. Ermon. Solving inverse problems in medical imaging with score-based generative models. Proceedings of the International Conference on Learning Representations, 2022.Google Scholar
• [57] Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole. Score-based generative modeling through stochastic differential equations. Proceedings of the International Conference on Learning Representations, 2021.Google Scholar
• [58] Y. Sun, Z. Wu, Y. Chen, B. T. Feng, and K. L. Bouman. Provable probabilistic imaging using score-based generative priors. IEEE Transactions on Computational Imaging 10:1290–1305, 2024.Crossref, Google Scholar
• [59] B. L. Trippe and R. E. Turner. Conditional density estimation with Bayesian normalising flows. Proceedings of the Second Workshop on Bayesian Deep Learning at Conference on Neural Information Processing Systems, 2017.Google Scholar
• [60] C. Villani. Optimal Transport: Old and New. Springer, Berlin, 2009.Crossref, Google Scholar
• [61] P. Vincent. A connection between score matching and denoising autoencoders. Neural Computation 23(7):1661–1674, 2011.Crossref, Google Scholar
• [62] J. Wen and J. Yang. Distributionally robust optimization via generative ambiguity modeling. Proceedings of the International Conference on Learning Representations, 2026.Google Scholar
• [63] A. Wibisono. Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem. Proceedings of the Conference on Learning Theory, 2093–3027, 2018.Google Scholar
• [64] C. Xu, X. Cheng, and Y. Xie. Invertible neural networks for graph prediction. IEEE Journal on Selected Areas in Information Theory 3(3):454–467, 2022.Crossref, Google Scholar
• [65] C. Xu, X. Cheng, and Y. Xie. Normalizing flow neural networks by JKO scheme. Proceedings of the Conference on Neural Information Processing Systems, 2023.Google Scholar
• [66] C. Xu, X. Cheng, and Y. Xie. Computing high-dimensional optimal transport by flow neural networks. Proceedings of the International Conference on Artificial Intelligence and Statistics, 2025.Google Scholar
• [67] C. Xu, J. Lee, X. Cheng, and Y. Xie. Flow-based distributionally robust optimization. IEEE Journal on Selected Areas in Information Theory 5:62–77, 2024.Crossref, Google Scholar
• [68] J. Yang, A. Orvieto, A. Lucchi, and N. He. Faster single-loop algorithms for minimax optimization without strong concavity. Proceedings of the International Conference on Artificial Intelligence and Statistics, 5485–5517, 2022.Google Scholar
• [69] J. Yu, J. Lee, Y. Xie, and X. Cheng. High-dimensional mean-field games by particle-based flow matching. Proceedings of the International Conference on Learning Representations, 2026.Google Scholar
• [70] L. Zhu and Y. Xie. Distributionally robust optimization via iterative algorithms in continuous probability spaces. Preprint, submitted December 29, https://arxiv.org/abs/2412.20556, 2024.Google Scholar