Discrete Spatial Diffusion: Intensity-Preserving Diffusion Modeling
Journal:
arXiv
Published Date:
May 3, 2025
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.
