Diffusion models on non-Euclidean manifolds turn out to be useful. We might imagine they are especially useful for PDEs or non-Gaussian spaces.
I only learned that these models existed about 5 minutes ago, so I won’t claim any depth of insight.
1 References
De Bortoli, Mathieu, Hutchinson, et al. 2022. “Riemannian Score-Based Generative Modelling.” Advances in Neural Information Processing Systems.
Jo, and Hwang. 2024. “Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processes.”
———. 2025. “Continuous Diffusion Model for Language Modeling.”
Jo, Kim, and Hwang. 2024. “Graph Generation with Diffusion Mixture.”