Neural denoising diffusion models with non-Gaussian increments

2024-04-16 — 2025-03-16

Wherein Poisson‑like increments are considered, and connections to Poisson Flow Generative Models via an extra‑dimension embedding parameter D are drawn, while perturbation‑based objectives are described.

approximation
Bayes
generative
Monte Carlo
neural nets
optimization
probabilistic algorithms
probability
score function
statistics
Figure 1

Placeholder. Diffusion models that don’t assume Gaussian increments in their noise processes. Are these useful?

Related but distinct: Diffusion models on discrete state spaces where the terminal distribution is categorical.

1 Poisson- and related Flow generative models

These models (Xu et al. 2022) are based on non-diffusive physics and are also used to simulate physical systems. A pop-sci explanation in Quanta magazine.

Unifying analyses—

Liu et al. (2023):

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for \(N\) dimensional data by embedding paths in \(N+D\) dimensional space while still controlling the progression with a simple scalar norm of the \(D\) additional variables. The new models reduce to PFGM when \(D=1\) and to diffusion models when \(D \rightarrow \infty\). The flexibility of choosing \(D\) allows us to trade off robustness against rigidity as increasing \(D\) results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models.[…] Code is available at https://github.com/Newbeeer/pfgmpp

Xu et al. (2023):

Since diffusion models (DM) and the more recent Poisson flow generative models (PFGM) are inspired by physical processes, it is reasonable to ask: Can physical processes offer additional new generative models? We show that the answer is Yes. We introduce a general family, Generative Models from Physical Processes (GenPhys), where we translate partial differential equations (PDEs) describing physical processes to generative models. We show that generative models can be constructed from \(s\)-generative PDEs ( \(s\) for smooth). GenPhys subsume the two existing generative models (DM and PFGM) and even give rise to new families of generative models, e.g., “Yukawa Generative Models” inspired from weak interactions. On the other hand, some physical processes by default do not belong to the GenPhys family, e.g., the wave equation and the Schrödinger equation, but could be made into the GenPhys family with some modifications. Our goal with GenPhys is to explore and expand the design space of generative models.

2 References

Chung, Kim, Mccann, et al. 2023. “Diffusion Posterior Sampling for General Noisy Inverse Problems.” In.
Han, Zheng, and Zhou. 2022. “CARD: Classification and Regression Diffusion Models.”
Hoogeboom, Nielsen, Jaini, et al. 2021. “Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions.” In Proceedings of the 35th International Conference on Neural Information Processing Systems. NIPS ’21.
Kim, and Ye. 2021. “Noise2Score: Tweedie’s Approach to Self-Supervised Image Denoising Without Clean Images.” In.
Liu, Luo, Xu, et al. 2023. “GenPhys: From Physical Processes to Generative Models.”
Nie, Zhu, You, et al. 2025. “Large Language Diffusion Models.”
Xu, Liu, Tegmark, et al. 2022. “Poisson Flow Generative Models.” In Proceedings of the 36th International Conference on Neural Information Processing Systems. NIPS ’22.
Xu, Liu, Tian, et al. 2023. “PFGM++: Unlocking the Potential of Physics-Inspired Generative Models.” In Proceedings of the 40th International Conference on Machine Learning. ICML’23.
Yang, Zhang, Song, et al. 2023. “Diffusion Models: A Comprehensive Survey of Methods and Applications.” ACM Computing Surveys.