$ρ$-Diffusion: A diffusion-based density estimation framework for
  computational physics
Maxwell X. Cai Kin Long Kelvin Lee
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.