Generative Modeling with the Yukawa Potential
By Pranav Kuppa, Max Wang, David Wei, Zani Xu
Diffusion models, the current state-of-the-art in image generation, have led the charge in generative modeling for several years. We provide a theoretical derivation and implementation of a new generative model based on the Yukawa potential. This model is the first of a new generation of models with nonzero birth rates, offering for more creative, and in some cases, accurate generation. The nonzero birth rate is a new variable in the generative process, offering great implications in applications without a constant number of particles. We focused on image generation as a proof of concept.
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Updates
Feb. 12, 2024
Update #1 (February): The coding portion of this project is on track. We have coded a baseline diffusion model from scratch, which we can alter structurally when creating the physics-informed models. We are also working on creating an altered version of the Poisson Flow Generative Model.
The math behind the physics-informed models we aim to create is far beyond our current knowledge, but we are gradually making our way through understanding it. We believe that Riemannian Manifolds would enable us to reduce the dimensionality of the nonlinear PDEs, so we spent most of our time learning about them and how to solve PDEs.