  Combinatorial optimization problems are widespread but inherently challenging
due to their discrete nature. The primary limitation of existing methods is
that they can only access a small fraction of the solution space at each
iteration, resulting in limited efficiency for searching the global optimal.To
overcome this challenge, diverging from conventional efforts of expanding the
solver's search scope, we focus on enabling information to actively propagate
to the solver through heat diffusion. By transforming the target function while
preserving its optima, heat diffusion facilitates information flow from distant
regions to the solver, providing more efficient navigation. Utilizing heat
diffusion, we propose a framework for solving general combinatorial
optimization problems.The proposed methodology demonstrates superior
performance across a range of the most challenging and widely encountered
combinatorial optimizations. Echoing recent advancements in harnessing
thermodynamics for generative artificial intelligence, our study further
reveals its significant potential in advancing combinatorial optimization.
