A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization

TL;DR

This paper introduces a novel diffusion model framework for unsupervised neural combinatorial optimization, enabling sampling from complex distributions without training data, and achieves state-of-the-art results on benchmarks.

Contribution

It presents a new diffusion-based approach that lifts the need for exact likelihoods, expanding the capabilities of neural combinatorial optimization methods.

Findings

Achieves state-of-the-art performance on benchmark problems.

Operates effectively in data-free settings.

Utilizes a loss that upper bounds reverse KL divergence.

Abstract

Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based approaches rely primarily on generative models that yield exact sample likelihoods. This work introduces a method that lifts this restriction and opens the possibility to employ highly expressive latent variable models like diffusion models. Our approach is conceptually based on a loss that upper bounds the reverse Kullback-Leibler divergence and evades the requirement of exact sample likelihoods. We experimentally validate our approach in data-free Combinatorial Optimization and demonstrate that our method achieves a new state-of-the-art on a wide range of benchmark problems.