Neural denoising diffusion models with non-Gaussian distributions

1 Poisson- and related Flow generative models

These (Xu et al. 2022) are based on non-diffusive physics but are also used to simulate physics

Popsci 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 $D\to \mathrm{\infty }$. 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 Language

See language models for using diffusion models in NLP.

3 References