$ρ$-Diffusion: A diffusion-based density estimation framework for computational physics

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. Moreover, we propose a novel hashing technique that allows $\rho$-Diffusion to be conditioned by arbitrary amounts of physical parameters of interest.