J. Kohler, L. Klein, and F. Noé. Equivariant Flows: exact likelihood generative learning for symmetric densities. arXiv:2006.02425 [physics, stat], June 2020. URL: http://arxiv.org/abs/2006.02425. Cited on page 6.
Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner. Gradient-based learning applied to document recognition. In Proceedings of the IEEE, volume 86 of number 11, pages 2278-2324, 1998. URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.7665. Cited on page 17.
H. Lee, J. Lu, and Y. Tan. Convergence of score-based generative modeling for general data distributions. In International Conference on Algorithmic Learning Theory, pages 946-985. PMLR, 2023. Cited on page 11.
J. H. Lim, N. B. Kovachki, R. Baptista, C. Beckham, K. Azizzadenesheli, J. Kossaifi, V. Voleti, J. Song, K. Kreis, J. Kautz, C. Pal, A. Vahdat, and A. Anandkumar. Score-based diffusion models in function space, 2023. DOI: 10.48550/ARXIV.2302.07400. Cited on page 1.
J. H. Lim, N. B. Kovachki, R. Baptista, C. Beckham, K. Azizzadenesheli, J. Kossaifi, V. Voleti, J. Song, K. Kreis, J. Kautz, C. Pal, A. Vahdat, and A. Anandkumar. Score-based diffusion models in function space, 2023. Cited on pages 3, 6.
A. Lou and S. Ermon. Reflected diffusion models. arXiv preprint arXiv:2304.04740, 2023. Cited on page 1.
C. Louizos, X. Shi, K. Schutte, and M. Welling. The functional neural process. Advances in Neural Information Processing Systems, 32, 2019. Cited on page 6.
A. Lugmayr, M. Danelljan, A. Romero, F. Yu, R. Timofte, and L. Van Gool. Repaint: inpainting using denoising diffusion probabilistic models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11461-11471, 2022. Cited on pages 5, 8-11.
I. Macêdo and R. Castro. Learning Divergence-Free and Curl-Free Vector Fields with Matrix-Valued Kernels. Pré-Publicações / A.: Pré-publicações. IMPA, 2010. Cited on pages 4, 6.
W. McKinney et al. Data structures for statistical computing in python. In Proceedings of the 9th Python in Science Conference, volume 445, pages 51-56. Austin, TX, 2010. Cited on page 13.
N. Miolane, N. Guigui, A. L. Brigant, J. Mathe, B. Hou, Y. Thanwerdas, S. Heyder, O. Peltre, N. Koep, H. Zaatiti, H. Hajri, Y. Cabanes, T. Gerald, P. Chauchat, C. Shewmake, D. Brooks, B. Kainz, C. Donnat, S. Holmes, and X. Pennec. Geomstats: a python package for riemannian geometry in machine learning. Journal of Machine Learning Research, 21(223):1-9, 2020. URL: http://jmlr.org/papers/v21/19-027.html. Cited on page 10.
B. Øksendal. Stochastic differential equations. In *Stochastic differential equations*, pages 65-84. Springer, 2003. Cited on page 4.
G. Papamakarios, E. Nalisnick, D. J. Rezende, S. Mohamed, and B. Lakshminarayanan. Normalizing flows for probabilistic modeling and inference. arXiv preprint arXiv:1912.02762, 2019. Cited on page 6.
A. Phillips, T. Seror, M. Hutchinson, V. De Bortoli, A. Doucet, and E. Mathieu. Spectral Diffusion Processes, Nov. 2022. URL: http://arxiv.org/abs/2209.14125. Cited on pages 3, 6, 1, 4, 5, 8.
J. Pidstrigach, Y. Marzouk, S. Reich, and S. Wang. Infinite-Dimensional Diffusion Models for Function Spaces, Feb. 2023. URL: http://arxiv.org/abs/2302.10130. Cited on pages 1, 3, 6.
D. Pollard. A User's Guide to Measure Theoretic Probability. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 2002. ISBN: 978-0-521-00289-9. URL: https://books.google.co.uk/books?id=B7Ch-c2G21MC. Cited on page 5.
A. Rahimi and B. Recht. Random features for large-scale kernel machines. Advances in neural information processing systems, 20, 2007. Cited on page 2.