Field Matching: an Electrostatic Paradigm to Generate and Transfer Data (ICML 2025)

This is the official Python implementation of the ICML 2025 paper Field Matching: an Electrostatic Paradigm to Generate and Transfer Data by Alexander Kolesov, Stepan Manukhov , Vladimir V. Palyulin and Alexander Korotin.

The repository contains reproducible PyTorch source code for computing maps for noise-to-data as well as data-to-data scenarios in high dimensions with neural networks. Examples are provided for toy 3D problems, unconditional data generation and unpaired translation problems.

Pre-requisites

The implementation is GPU-based. Single GPU GTX 1080 ti is enough to run each particular experiment. We tested the code with torch==2.1.1+cu121. The code might not run as intended in older/newer torch versions. Versions of other libraries are specified in requirements.txt.

Repository structure

All the experiments are issued in the form of pretty self-explanatory jupyter notebooks.

• src - auxiliary source code for the constructing of the neural network model.
• notebooks/EFMToy.ipynb - the notebook of 3D illustrative examples
• notebooks/EFMCMGeneration.ipynb - the notebook of the noise-to-image generation on Colored MNIST dataset.
• notebooks/EFMCIFAR10Generation.ipynb - the notebook of the noise-to-image generation on CIFAR-10 dataset.
• 'notebooks/EFMTranslation.ipynb' - the notebook for data-to-data scenario.
• 'poster' - the poster presented at ICML 2025.
• 'slides' - slides presented at ICML 2025.

pip install -r requirements.txt

• Download MNIST dataset

• Donwload CIFAR10 dataset

• Set downloaded dataset in appropriate subfolder in data/.

Unconditional Data Generation on Colored MNIST and CIFAR-10

Unpaired dataset translation from digits 3 to digits 2

Credits

• Weights & Biases developer tools for machine learning;
• UNet architecture for map network;
• Inkscape for the awesome editor for vector graphics;