Dongjun Kim, Seungjae Shin, Kyungwoo Song, Wanmo Kang, and Il-Chul Moon. Soft truncation: A universal training technique of score-based diffusion model for high precision score estimation. In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvari, Gang Niu, and Sivan Sabato (eds.), Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, pp. 11201-11228. PMLR, 17-23 Jul 2022b.
Diederik P Kingma, Tim Salimans, Ben Poole, and Jonathan Ho. Variational diffusion models. In A. Beygelzimer, Y. Dauphin, P. Liang, and J. Wortman Vaughan (eds.), Advances in Neural Information Processing Systems, 2021. URL https://openreview.net/forum?id=2LdBqxc1Yv.
Zhifeng Kong, Wei Ping, Jiaji Huang, Kexin Zhao, and Bryan Catanzaro. Diffwave: A versatile diffusion model for audio synthesis. In International Conference on Learning Representations, 2021.
Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Neural operator: Learning maps between function spaces. arXiv preprint arXiv:2108.08481, 2021.
Tuomas Kynkänniemi, Tero Karras, Miika Aittala, Timo Aila, and Jaakko Lehtinen. The role of imagenet classes in fréchet inception distance. arXiv preprint arXiv:2203.06026, 2022.
Yann LeCun, Corinna Cortes, and CJ Burges. Mnist handwritten digit database. ATT Labs [Online]. Available: http://yann.lecun.com/exdb/mnist, 2, 2010.
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations. arXiv preprint arXiv:2010.08895, 2020.
Jae Hyun Lim, Nikola B Kovachki, Ricardo Baptista, Christopher Beckham, Kamyar Azizzadenesheli, Jean Kossaifi, Vikram Voleti, Jiaming Song, Karsten Kreis, Jan Kautz, et al. Score-based diffusion models in function space. arXiv preprint arXiv:2302.07400, 2023.
Jinglin Liu, Chengxi Li, Yi Ren, Feiyang Chen, and Zhou Zhao. Diffsinger: Singing voice synthesis via shallow diffusion mechanism. Proceedings of the AAAI Conference on Artificial Intelligence, 36(10):11020-11028, Jun. 2022.
Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaou Tang. Deep learning face attributes in the wild. In Proceedings of International Conference on Computer Vision (ICCV), December 2015.
Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101, 2017.
Shitong Luo and Wei Hu. Diffusion probabilistic models for 3d point cloud generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2837-2845, June 2021.
Annie Millet, David Nualart, and Marta Sanz. Time reversal for infinite-dimensional diffusions. Probability theory and related fields, 82(3):315-347, 1989.
Sarthak Mittal, Guillaume Lajoie, Stefan Bauer, and Arash Mehrjou. From points to functions: Infinite-dimensional representations in diffusion models. In ICLR Workshop on Deep Generative Models for Highly Structured Data, 2022.
Isaac Pesenson. A sampling theorem on homogeneous manifolds. Transactions of the American Mathematical Society, 352(9):4257-4269, 2000.
Angus Phillips, Thomas Seror, Michael Hutchinson, Valentin De Bortoli, Arnaud Doucet, and Emile Mathieu. Spectral diffusion processes. arXiv preprint arXiv:2209.14125, 2022.
Jakiw Pidstrigach, Youssef Marzouk, Sebastian Reich, and Sven Wang. Infinite-dimensional diffusion models for function spaces. arXiv preprint arXiv: 2302.10130, 2023.
Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text-conditional image generation with clip latents, 2022. URL https://arxiv.org/abs/2204.06125.