# Boosting Cross-problem Generalization in Diffusion-Based Neural Combinatorial Solver via Inference Time Adaptation

arXiv: https://arxiv.org/abs/2502.12188 · HTML: https://mlsanity.com/paper/2502.12188/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 30 of its 42 references that are in the map.
- First posted on arXiv 15 Feb 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (2020)
- [DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems](https://mlsanity.com/paper/2210.04123/) (2022)
- [Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimization](https://mlsanity.com/paper/2205.13209/) (2022)
- [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024)
- [Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2012.10638/) (2020)
- [A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization](https://mlsanity.com/paper/2406.01661/) (2024)
- [Fast T2T: Optimization Consistency Speeds Up Diffusion-Based Training-to-Testing Solving for Combinatorial Optimization](https://mlsanity.com/paper/2502.02941/) (2025)
- [A Survey for Solving Mixed Integer Programming via Machine Learning](https://mlsanity.com/paper/2203.02878/) (2022)
- [Understanding and Improving Training-free Loss-based Diffusion Guidance](https://mlsanity.com/paper/2403.12404/) (2024)
- [ASP: Learn a Universal Neural Solver!](https://mlsanity.com/paper/2303.00466/) (2023)
- [Cross-Problem Learning for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2404.11677/) (2024)

## Built on by (most cited first, 1 of 1)

- [Constrained Graph Diffusion for Mixed Integer Optimization](https://mlsanity.com/paper/2608.13079/) (2026)

## Abstract (arXiv)

Diffusion-based Neural Combinatorial Optimization (NCO) has demonstrated effectiveness in solving NP-complete (NPC) problems by learning discrete diffusion models for solution generation, eliminating hand-crafted domain knowledge. Despite their success, existing NCO methods face significant challenges in both cross-scale and cross-problem generalization, and high training costs compared to traditional solvers. While recent studies on diffusion models have introduced training-free guidance approaches that leverage pre-defined guidance functions for conditional generation, such methodologies have not been extensively explored in combinatorial optimization. To bridge this gap, we propose a training-free inference time adaptation framework (DIFU-Ada) that enables both the zero-shot cross-problem transfer and cross-scale generalization capabilities of diffusion-based NCO solvers without requiring additional training. We provide theoretical analysis that helps understanding the cross-problem transfer capability. Our experimental results demonstrate that a diffusion solver, trained exclusively on the Traveling Salesman Problem (TSP), can achieve competitive zero-shot transfer performance across different problem scales on TSP variants, such as Prize Collecting TSP (PCTSP) and the Orienteering Problem (OP), through inference time adaptation.