Geometric Trajectory Diffusion Models (NeurIPS 2024)

Jiaqi Han, Minkai Xu, Aaron Lou, Haotian Ye, Stefano Ermon

Stanford University

Introduction

We introduce Geometric Trajectory Diffusion Models (GeoTDM), a generative model that captures the distribution of geometric trajectories, i.e., the temporal evolution of a geometric system. GeoTDM extends geometric diffusion models from static states to temporal dynamics by directly modeling the joint distribution of a sequence of frames. More importantly, GeoTDM features an SE(3)-equivariant spatio-temporal graph neural network and a carefully designed prior parameterization, enabling the preservation of physical symmetry and expressive distribution modeling.

GeoTDM demonstrates strong performance in modeling geometric trajectories across various domains, including, e.g., molecular dynamics, physical simulation, and pedestrian trajectory forecasting, in both unconditional and conditional generation settings.

Dependencies

We use python==3.8.18 for our experiments with the following core packages:

torch==1.13.0
torch-geometric==2.4.0
scikit-learn==1.3.2
networkx==3.1
pandas==2.0.3
einops==0.7.0

Other packages like wandb, torch-scatter, torch-sparse, torch-kmeans are also recommended to install for full functionality.

Experiments

Physical Simulation

Data Generation

Generate the dataset by running gen_data.sh under datasets/datagen folder.

Conditional Generation

Training, inference, and evaluation (all in one script):

python -m torch.distributed.launch \
    --nproc_per_node=4 \
    --master_port 16888 \
    experiments/nbody_train.py \
    --train_yaml_file configs/nbody_train_cond.yaml

By default, we use 4 GPUs for training. You can change the number of GPUs by modifying --nproc_per_node. You can also enable wandb to monitor training by changing no_wandb to False in the config file.

Unconditional Generation

Training:

python -m torch.distributed.launch \
    --nproc_per_node=4 \
    --master_port 16888 \
    experiments/nbody_train.py \
    --train_yaml_file configs/nbody_train_uncond.yaml

Inference:

python experiments/nbody_sampling.py --eval_yaml_file configs/nbody_sampling.yaml

Evaluation:

python -m experiments.scores --path outputs/nbody_GeoTDM_uncond_eval/samples.pkl

Molecular Dynamics

Data Preparation

Download the MD17 dataset in .npz format from here. The dataset should be placed in data/md17.

Conditional Generation

Training, inference, and evaluation (all in one script):

python -m torch.distributed.launch \
    --nproc_per_node=4 \
    --master_port 16888 \
    experiments/md17_train.py \
    --train_yaml_file configs/md17_train_cond.yaml

Unconditional Generation

Training:

python -m torch.distributed.launch \
    --nproc_per_node=4 \
    --master_port 16888 \
    experiments/md17_train.py \
    --train_yaml_file configs/md17_train_uncond.yaml

Inference:

python experiments/md17_sampling.py --eval_yaml_file configs/md17_sampling.yaml

Evaluation:

python -m experiments.scores --path outputs/md17_aspirin_GeoTDM_uncond_eval/samples.pkl --chem

Pedestrian Trajectory Forecasting

Data Preparation

Follow the instructions here to download and preprocess the data. Then move the preprocessed files in the folder processed_data_diverse into data/eth.

Conditional Generation

Training, inference, and evaluation (all in one script):

python -m torch.distributed.launch \
    --nproc_per_node=4 \
    --master_port 16888 \
    experiments/eth_train_new.py \
    --train_yaml_file configs/eth_train_new.yaml

Generated Samples

Citation

Please consider citing our work if you find it useful:

@article{han2024geometric,
  title={Geometric Trajectory Diffusion Models},
  author={Han, Jiaqi and Xu, Minkai and Lou, Aaron and Ye, Haotian and Ermon, Stefano},
  journal={arXiv preprint arXiv:2410.13027},
  year={2024}
}

Contact

If you have any question, welcome to contact me at:

Jiaqi Han: [email protected]

Acknowledgment

This repo is built upon several great codebases, including guided diffusion and EqMotion. We thank the authors for their great work and open-sourcing the code.