This is the official repo for Unsupervised Diffusion Solver for Combinatorial Optimization via Combinatorial Adjoint Matching, ICML 2026. If you have any question, please contact us at: shengyuf@cs.cmu.edu.

Install PyTorch matching your CUDA version (example below uses torch 2.11.0 + CUDA 12.8; adjust versions accordingly):

pip install torch==2.11.0 --index-url https://download.pytorch.org/whl/cu128
pip install pyg_lib torch_scatter torch_sparse -f https://data.pyg.org/whl/torch-2.11.0+cu128.html
pip install torch_geometric
pip install -r requirements.txt

Compile the TSP utils:

cd utils/cython_merge
python setup.py build_ext --inplace
cd -

Compile the CVRP utils:

cd utils/c_classic
make
cd -

You can download our data & checkpoints from huggingface.

To summarize our data sources:

• TSP & MIS (ER): DIFUSCO,
• MIS (RB) & MCut: DiffUCO,
• CVRP: ML4CO-Bench-101.

Also, you can find the data generators at FrontierCO.

Edit scripts/config.sh to set your data directory and number of GPUs:

export DATADIR=/path/to/your/data
export PROCESSES=#GPUs

Launch any script directly:

bash scripts/mis/mis_er_cam.sh
bash scripts/mis/mis_rb_small_cam.sh
bash scripts/mis/mis_rb_large_cam.sh
bash scripts/tsp/tsp_500_cam.sh
bash scripts/tsp/tsp_1000_cam.sh
bash scripts/mcut/mcut_ba_large_cam.sh
bash scripts/cvrp/cvrp_100_cam.sh

To run inference on your trained models, make two changes to the script:

1. Remove --do_train
2. Set --num_processes 1 in scripts/config.sh (important: ensures fairness in time measurement)

For mis_er_cam.sh, if you want to test ER-[9000-11000], you need to set --num_t 200 and update --test_path $DATADIR/MIS/ER_large_test.

You can also specify the --checkpoint arg for testing existing models, for example:

--checkpoint CAM_models/mis_rb_small_cam/cam/best.pt

@misc{feng2026unsuperviseddiffusionsolvercombinatorial,
    title={Unsupervised Diffusion Solver for Combinatorial Optimization via Combinatorial Adjoint Matching}, 
    author={Shengyu Feng and Tarun Suresh and Yiming Yang},
    year={2026},
    eprint={2605.30920},
    archivePrefix={arXiv},
    primaryClass={cs.LG},
    url={https://arxiv.org/abs/2605.30920}, 
}