Discrete Spatial Diffusion: Intensity-Preserving Diffusion Modeling

TL;DR

This paper introduces Discrete Spatial Diffusion, a novel diffusion model operating in discrete spaces that preserves particle counts, enabling applications in scientific domains with strict conservation laws, demonstrated through image synthesis and material microstructure generation.

Contribution

The paper presents a new diffusion framework based on a discrete jump process that maintains particle counts, extending diffusion modeling to applications requiring strict conservation laws.

Findings

Successfully performs image synthesis, inpainting, and class conditioning with intensity preservation.

Generates realistic microstructures of porous rocks and battery electrodes under mass conservation constraints.

Achieves state-of-the-art metrics in transport and electrochemical performance evaluations.

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.