Fast 3D Diffusion for Scalable Granular Media Synthesis

Simulating granular media, using Discrete Element Method is a computationally intensive task. This is especially true during initialization phase, which dominates total simulation time because of large displacements involved and associated kinetic energy. We overcome this bottleneck with a novel generative pipeline based on 3D diffusion models that directly synthesizes arbitrarily large granular assemblies in their final and physically realistic configurations. The approach frames the problem as a 3D generative modeling task, consisting of a two-stage pipeline. First a diffusion model is trained to generate independent 3D voxel grids representing granular media. Second, a 3D inpainting model, adapted from 2D inpainting techniques using masked inputs, stitches these grids together seamlessly, enabling synthesis of large samples with physically realistic structure. The inpainting model explores several masking strategies for the inputs to the underlying UNets by training the network to infer missing portions of voxel grids from a concatenation of noised tensors, masks, and masked tensors as input channels. The model also adapts a 2D repainting technique of re-injecting noise scheduler output with ground truth to provide a strong guidance to the 3D model. This along with weighted losses ensures long-term coherence over generation of masked regions. Both models are trained on the same binarized 3D occupancy grids extracted from small-scale DEM simulations, achieving linear scaling of computational time with respect to sample size. Quantitatively, a 1.2 m long ballasted rail track synthesis equivalent to a 3-hour DEM simulation, was completed under 20 seconds. The generated voxel grids can also be post-processed to extract grain geometries for DEM-compatibility as well, enabling physically coherent, real-time, scalable granular media synthesis for industrial applications.