{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/r-diffusion-a-diffusion-based-density","title":"$ρ$-Diffusion: A diffusion-based density estimation framework for computational physics","arxiv_id":"2312.08153","date":"2023-12-13","proceeding":null,"authors":["Maxwell X. Cai","Kin Long Kelvin Lee"],"abstract":"In physics, density $\\rho(\\cdot)$ is a fundamentally important scalar function to model, since it describes a scalar field or a probability density function that governs a physical process. Modeling $\\rho(\\cdot)$ typically scales poorly with parameter space, however, and quickly becomes prohibitively difficult and computationally expensive. One promising avenue to bypass this is to leverage the capabilities of denoising diffusion models often used in high-fidelity image generation to parameterize $\\rho(\\cdot)$ from existing scientific data, from which new samples can be trivially sampled from. In this paper, we propose $\\rho$-Diffusion, an implementation of denoising diffusion probabilistic models for multidimensional density estimation in physics, which is currently in active development and, from our results, performs well on physically motivated 2D and 3D density functions. 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