Neural denoising diffusion models with non-Gaussian distributions

2024-04-16 — 2025-04-03

approximation
Bayes
classification
generative
Monte Carlo
neural nets
optimization
probabilistic algorithms
probability
score function
statistics
Wherein neural denoising diffusion models are examined on non‑Euclidean manifolds, their applicability to partial differential equations and non‑Gaussian spaces is outlined, and a recent discovery by the author is noted.

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.

Figure 1

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.”
Li, Yu, He, et al. 2024. “SPD-DDPM: Denoising Diffusion Probabilistic Models in the Symmetric Positive Definite Space.” Proceedings of the AAAI Conference on Artificial Intelligence.