Discrete Spatial Diffusion: Intensity-Preserving Diffusion Modeling

Javier E. Santos, Agnese Marcato, Roman Colman, Nicholas Lubbers, Yen Ting Lin

Keywords: Diffusion models, physics, spatial diffusion, continuous-time discrete-state Markov process, mass conservation, intensity conservation, scientific data

TL;DR: This paper presents Discrete Spatial Diffusion, a generative model for discrete-state data that ensures mass conservation, enabling applications in scientific domains like materials science, also demonstrating results on popular image benchmarks.

Abstract: 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.

Primary Area: Machine learning for sciences (e.g. climate, health, life sciences, physics, social sciences)

Submission Number: 23102