Three-dimensional digital reconstruction of porous media presents a fundamental challenge in geoscience, requiring simultaneous resolution of fine-scale pore structures while capturing representative elementary volumes. We introduce a computational framework that addresses this challenge through latent diffusion models operating within the EDM framework. Our approach reduces dimensionality via a custom variational autoencoder trained in binary geological volumes, improving efficiency and also enabling the generation of larger volumes than previously possible with diffusion models. A key innovation is our controlled unconditional sampling methodology, which enhances distribution coverage by first sampling target statistics from their empirical distributions, then generating samples conditioned on these values. Extensive testing on four distinct rock types demonstrates that conditioning on porosity - a readily computable statistic - is sufficient to ensure a consistent representation of multiple complex properties, including permeability, two-point correlation functions, and pore size distributions. The framework achieves better generation quality than pixel-space diffusion while enabling significantly larger volume reconstruction (256-cube voxels) with substantially reduced computational requirements, establishing a new state-of-the-art for digital rock physics applications.

翻译：三维多孔介质的数字化重建是地球科学领域的一项基础性挑战，它要求同时解析微米级孔隙结构并捕获具有代表性的基本体积单元。我们提出了一种计算框架，通过在EDM框架内运行的潜在扩散模型来解决这一难题。我们的方法通过一个在二值化地质体数据上训练的自定义变分自编码器实现降维，不仅提高了效率，还能生成比以往扩散模型所能处理的更大体积样本。一项关键创新是我们的可控无条件采样方法，该方法首先从经验分布中采样目标统计量，然后基于这些数值生成条件样本，从而增强了分布覆盖范围。在四种不同岩石类型上的大量测试表明，以孔隙度（一种易于计算的统计量）为条件，足以确保多种复杂属性（包括渗透率、两点相关函数和孔径分布）的表征一致性。该框架在实现比像素空间扩散模型更优生成质量的同时，能以显著降低的计算需求完成更大体积（256立方体素）的重建，从而为数字岩石物理应用确立了新的技术标杆。