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.

翻译：在物理学中，密度函数$\rho(\cdot)$是建模中至关重要的标量函数，因为它描述了一个标量场或控制物理过程的概率密度函数。然而，$\rho(\cdot)$的建模通常随参数空间增大而性能退化，并迅速变得极其困难且计算成本高昂。一种有前景的解决方案是利用常用于高保真图像生成的去噪扩散模型的能力，从现有科学数据中参数化$\rho(\cdot)$，从而可以轻松从中采样新样本。本文提出$\rho$-Diffusion——一种将去噪扩散概率模型应用于物理学中多维密度估计的实现方法。该方法目前正在积极开发中，根据我们的结果，在物理驱动的二维和三维密度函数上表现优异。此外，我们提出了一种新颖的哈希技术，使$\rho$-Diffusion能够根据任意数量的物理参数进行条件化。