Matérn Noise for Triangulation-Agnostic Flow Matching on Meshes

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Official code release for Matérn Noise for Triangulation-Agnostic Flow Matching on Meshes, by Tianshu Kuai, Arman Maesumi, Daniel Ritchie, and Noam Aigerman, published in ACM Transactions on Graphics (SIGGRAPH 2026).

Installation

# create conda environment
conda create -y -n matern_fm python=3.9
conda activate matern_fm

# install torch (other versions also work)
# install the version that works for your machine
pip install torch==2.1.2 torchvision==0.16.2 --index-url https://download.pytorch.org/whl/cu121

# install other dependencies
pip install -r requirements.txt

# install torch_mesh_ops
git clone https://github.com/ArmanMaesumi/torch_mesh_ops
cd torch_mesh_ops && python setup.py install
cd .. && rm -rf torch_mesh_ops

# install cholespy (custom version that supports solver caching)
git clone --recursive https://github.com/kts707/cholespy.git
pip install ./cholespy
rm -rf ./cholespy

Note that we install the custom version of the cholespy package above. It supports caching the cholespy solvers of all source meshes in the dataset before training. This avoids repeatedly creating solvers on the fly during training (can significantly reduce total training time in arbitrary source setup). If you wish to use the official cholespy package, then use code in official_cholespy branch.

Matérn noise sampling

We provide stand-alone example scripts for sampling Matérn noise on a triangle mesh.

# Uses potpourri3d and cholespy
python matern_noise/sample_matern_noise_pp3d.py --mesh <mesh.obj> --screening_term 100.0 --sigma 5.0

# Uses torch_mesh_ops and cholespy
python matern_noise/sample_matern_noise_tmo.py --mesh <mesh.obj> --screening_term 100.0 --sigma 5.0

Run our pre-trained models

Download our pre-trained checkpoints.

bash demo/download_weights.sh

Test our pre-trained models on the source meshes under demo/meshes. The generated deformed meshes are stored under demo/results. The SMPL human models are trained on a dataset of yoga poses, and the Stanford bunny and Fish models are trained on a dataset of elastic equilibrium states (see Datasets section for more details).

# Single source model on SMPL
bash demo/single_source_smpl.sh

# Single source model on Stanford bunny
bash demo/single_source_stanford_bunny.sh

# Single source model on Fish
bash demo/single_source_fish.sh

# Arbitrary 3D human source model (trained on a dataset of yoga poses)
bash demo/arbitrary_source_smpl.sh

Training

Datasets

Download our preprocessed dataset files here and put them under data folder.

If you would like to create the datasets yourself, refer to PoissonNet's instructions on preparing the SMPL dataset (yoga poses). We also provide scripts to create datasets by simulating the equilibrium states of an elastic object in this repository.

Run training

All config files are stored in the configs folder. They assume training on a single NVIDIA H100 GPU (80 GB VRAM). To fit on a GPU with less VRAM, simply reduce the batch_size in the configs and enable gradient accumulation (accumulate_grad_batches) to keep the same effective batch size.

# Single source model on SMPL
python train/train_single_source.py configs/moyo_fixed_source.yaml

# Single source model on Stanford bunny
python train/train_single_source.py configs/stanford_bunny.yaml

# Single source model on Fish
python train/train_single_source.py configs/fish.yaml

# Arbitrary 3D human source model
python train/train_arbitrary_source.py configs/moyo_arbitrary_source.yaml

Test trained models

# Single source model on SMPL
bash test/test_single_source_smpl.sh configs/moyo_fixed_source.yaml single_source_test_results

# Single source model on Stanford bunny
bash test/test_single_source_stanford_bunny.sh configs/stanford_bunny.yaml single_source_test_results

# Single source model on Fish
bash test/test_single_source_fish.sh configs/fish.yaml single_source_test_results

# Arbitrary 3D human source model
bash test/test_arbitrary_source.sh configs/moyo_arbitrary_source.yaml humanoids_test_results

Acknowledgement

The neural network architecture code was adapted from PoissonNet, and the Flow Matching pipeline was from Flow Matching. A big thanks to their work and efforts in releasing the code.

Citation

If you find our work useful in your research, please consider citing it:

@article{kuai2026matern,
  author    = {Kuai, Tianshu and Maesumi, Arman and Ritchie, Daniel and Aigerman, Noam},
  title     = {Matérn Noise for Triangulation-Agnostic Flow Matching on Meshes},
  journal   = {ACM Transactions on Graphics (TOG)},
  volume    = {45},
  number    = {4},
  pages     = {1--17},
  year      = {2026},
  publisher = {ACM New York, NY, USA}
}

License

This project is under the MIT license.