MG-Diff brings discrete Morse and cobordism theory into graph diffusion models for spatio-temporal forecasting and graph regeneration
The work argues that low-dimensional topology such as Morse theory offers a strong, complementary, and largely unexplored perspective for machine learning; it introduces concepts from cobordism theory and harnesses discrete Morse theory tools to improve graph diffusion models through a pipeline called MG-Diff, derives theoretical guarantees and sufficient conditions showing that under a positive decision-gap the Morse-theoretic tools and their use for induced diffusion guidance are stable under small perturbations, and illustrates the utility of discrete Morse theory for spatio-temporal graph forecasting and graph regeneration.