Discrete Spatial Diffusion: Intensity-Preserving Diffusion Modeling

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

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, because these models typically operate in continuous intensity spaces—diffusing independently per pixel and color channel—they are fundamentally ill-suited for applications where quantities such as particle counts or material units are inherently discrete and governed by strict conservation laws like mass preservation, which limits 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 mass in both forward and reverse diffusion processes. By using spatial diffusion to achieve mass preservation, 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 widely-used image benchmarks, with the ability to condition on image intensity. Additionally, we highlight its applicability to domain-specific scientific data for materials microstructure, bridging the gap between diffusion models and mass-conditioned scientific applications.

Primary Area: Deep Learning->Generative Models and Autoencoders

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

Submission Number: 15104