HOG-Diff: Higher-Order Guided Diffusion for Graph Generation

Official Implementations of HOG-Diff: Higher-Order Guided Diffusion for Graph Generation (ICLR 2026).

Yiming Huang, Tolga Birdal

📄 arXiv · 🌐 Project page

In this work, we propose a novel Higher-order Guided Diffusion (HOG-Diff) model that follows a coarse-to-fine generation curriculum and is guided by higher-order information, enabling the progressive generation of authentic graphs with inherent topological structures.

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Environment Setup

This code was tested with PyTorch 2.0.0, cuda 11.8 and torch_geometrics 2.6.1

1️⃣ Download anaconda/miniconda if needed

2️⃣ Create and Activate a Python Virtual Environment

conda create -n hogdiff python=3.9
conda activate hogdiff

3️⃣ Install Dependencies

Install PyTorch 2.0.0 matching your CUDA version (see the PyTorch previous-versions page), then the matching PyG extensions, then the rest:

# PyTorch (adjust cu118 / cu117 / cpu to your platform)
pip install torch==2.0.0+cu118 torchvision==0.15.1+cu118 --index-url https://download.pytorch.org/whl/cu118

# PyG extensions (pick the wheel for your torch / CUDA build)
pip install torch_geometric==2.6.1
pip install torch_scatter==2.1.1 -f https://data.pyg.org/whl/torch-2.0.0+cu118.html

# Remaining dependencies
pip install -r requirements.txt

4️⃣ Compile the ORCA Program (for Graph Generation Evaluation)

For evaluating generic graph generation tasks, compile the ORCA program by running the following command:

cd evaluation/orca 
g++ -O2 -std=c++11 -o orca orca.cpp

Data Setup

Datasets should be placed under ./data/<dataset_name>/. Supported datasets:

Dataset	Type	Source
qm9	molecular	QM9
zinc250k	molecular	ZINC250k
moses	molecular	MOSES benchmark
guacamol	molecular	GuacaMol benchmark
community_small (cs), ego_small (ego), enzymes, sbm	generic graphs	preprocessed .pkl bundled with this repo under data/<name>/

For molecular datasets, the raw files will be auto-processed into data/<dataset>/processed/ on first run.

By default, checkpoints and processed data are resolved via the CKPT_ROOT and DATA_ROOT environment variables. Both default to the project root.

5️⃣ (Optional) Local environment overrides

Copy the template to activate per-machine overrides (wandb entity, CUDA device, custom CKPT_ROOT/DATA_ROOT, etc.). The actual env_config.yaml is gitignored.

cp configs/env_config.example.yaml configs/env_config.yaml
# edit configs/env_config.yaml as needed

Pretrained Checkpoints

Download the pretrained checkpoints and place them under checkpoints/<dataset>/<dataset>.pth (or set CKPT_ROOT to the directory that contains your checkpoints/ tree). The configs in configs/<dataset>.yaml default to this layout.

Download link: TBD — will be released soon.

To use a custom ckpt, pass --ckpt /absolute/or/relative/path.pth to main.py.

Running Experiments

To train and sample graphs using HOG-Diff, use the following commands:

CUDA_VISIBLE_DEVICES=0 python main.py --config config_name --mode train_ho
CUDA_VISIBLE_DEVICES=0 python main.py --config config_name --mode train_OU
CUDA_VISIBLE_DEVICES=0 python main.py --config config_name --mode sample

Replace config_name with the appropriate configuration file.

Using the Filtering Operation Standalone

The higher-order graph filtering described in the paper (Prop. 2) lives in utils/ho_utils.py as two self-contained functions with no project dependencies — you can import them in your own pipeline:

import torch
from utils.ho_utils import cell_complex_filter, simplicial_complex_filter

adj = torch.tensor([[0, 1, 1, 0],
                    [1, 0, 1, 0],
                    [1, 1, 0, 1],
                    [0, 0, 1, 0]], dtype=torch.float)

# Cell-complex filter: keep edges on a cycle of length ≤ max_media_size
ccf = cell_complex_filter(adj, max_media_size=3)

# Simplicial-complex filter: keep edges inside cliques of size ≥ min_size
scf = simplicial_complex_filter(adj, min_size=3)

# Both accept a batch [B, N, N] too; max_node_num pads each output if given.
batch = torch.stack([adj, adj])
cell_complex_filter(batch, max_node_num=8)   # → [2, 8, 8]

To plug in a custom filter, write any function with the same signature (graph_tensor, max_node_num=None, ...) -> torch.Tensor and pass it where ho_utils.cell_complex_filter is called in utils/dataloader.py.

Citation

Please cite our work if you find our code/paper is useful to your work. :

@inproceedings{hogdiff-ICLR2026,
  title={HOG-Diff: Higher-Order Guided Diffusion for Graph Generation},
  author={Huang, Yiming and Birdal, Tolga},
  booktitle={The Fourteenth International Conference on Learning Representations},
  year={2026}
}

🍀 Thank you for your interest in our work. 🍀

If you have any questions or encounter any issues while using our code, please contact yimingh999@gmail.com. Enjoy 😊