Parallel Tempering for Diffusion-Based Combinatorial Optimization
When applying discrete diffusion models to combinatorial optimization, independent sampling improves solution quality but incurs substantial computational overhead. This work proposes PT-Denoise, an inference method that introduces parallel tempering into the diffusion denoising phase for the first time. Without retraining, it enables adaptive inter-trajectory interactions: low-energy trajectories concentrate at lower temperatures for fine-grained search, while high-energy states continue exploring at higher temperatures, thereby dynamically allocating sampling resources. Evaluated on graph-structured combinatorial optimization tasks, the proposed method significantly enhances the quality of the best solutions found with minimal additional computational cost.