Discrete Spatial Diffusion: Intensity-Preserving Diffusion Modeling
This addresses a limitation in diffusion models for scientific workflows requiring strict conservation, such as in materials science, though it is an incremental improvement by adapting existing methods to discrete domains.
The paper tackled the problem of generative diffusion models being ill-suited for discrete quantities with conservation laws by proposing Discrete Spatial Diffusion (DSD), a framework that operates in discrete spatial domains while strictly preserving particle counts, and demonstrated its effectiveness in image synthesis and scientific applications like porous rock and battery electrodes with quantitative metrics.
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result, they are fundamentally ill-suited for applications involving inherently discrete quantities-such as particle counts or material units-that are constrained by strict conservation laws like mass conservation, limiting their applicability in scientific workflows. To address this limitation, we propose Discrete Spatial Diffusion (DSD), a framework based on a continuous-time, discrete-state jump stochastic process that operates directly in discrete spatial domains while strictly preserving particle counts in both forward and reverse diffusion processes. By using spatial diffusion to achieve particle conservation, we introduce stochasticity naturally through a discrete formulation. We demonstrate the expressive flexibility of DSD by performing image synthesis, class conditioning, and image inpainting across standard image benchmarks, while exactly conditioning total image intensity. We validate DSD on two challenging scientific applications: porous rock microstructures and lithium-ion battery electrodes, demonstrating its ability to generate structurally realistic samples under strict mass conservation constraints, with quantitative evaluation using state-of-the-art metrics for transport and electrochemical performance.