Parallel Tempering for Diffusion-Based Combinatorial Optimization

2026-09-29

AI Summary

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.

Abstract

Discrete diffusion models have emerged as a powerful paradigm for solving combinatorial optimization (CO) problems on graphs by learning to sample high-quality solutions. A common inference-time approach is to generate multiple candidate solutions independently and return the best-performing sample, improving solution quality at the expense of an increase in computational cost. In this work, we introduce PT-Denoise, an inference-time procedure that allows these concurrent denoising trajectories to interact through parallel tempering, without requiring retraining or fine-tuning of the underlying denoiser. Our method assigns a temperature to each diffusion process and allows processes to swap temperatures based on their relative performance. This dynamically reallocates promising, low-energy trajectories to colder, more concentrated sampling regimes while allowing higher-energy states to escape local minima through randomized exploration. Experiments on canonical graph-structured CO problems show that our approach consistently improves the quality of the best solution found, while only adding minimal computational overhead.

Problem

• Combinatorial Optimization
• Discrete Diffusion Models
• Parallel Tempering
• Graph Problems

Innovation

• Parallel Tempering
• Discrete Diffusion Models
• Combinatorial Optimization
• Inference-time Procedure
• PT-Denoise