Title: One-Step Diffusion Solver for Non-binary Integer Linear Programming
Primary area: generative models
Keywords: one-step diffusion model, integer linear programming

Abstract: Integer linear programming, a fundamental NP-hard problem with broad applications in science and engineering, has gained growing attention in the machine learning community. Yet, progress on effective end-to-end solvers remains limited, largely due to difficulties in enforcing constraints and integrality. Most existing work focuses on binary integer linear programming problems, while generalizing to bounded, non-binary cases often requires transformations that significantly increase problem size and computational costs. Even for purely binary problems, inference time is often prohibitively long, restricting applicability to real-world scenarios. To tackle the aforementioned problems, we propose three one-step diffusion-based approaches, i.e., CMILP, SCMILP and MFILP, inspired by the popular consistency, shortcut and meanflow training techniques. Our methods can further handle non-binary integer problems using a newly proposed iterative integer projection (IIP) layer, eliminating the need for the costly problem transformation. To further improve the solution quality, an objective-guided sampling with momentum scheme is proposed. Experiments demonstrate that our approach outperforms existing learning-based methods on both binary and non-binary instances and shows strong scalability compared to traditional solvers. Source code and detailed protocols will be made publicly available.