This is the official Python implementation of the ICLR 2026 paper Interaction Field Matching: Overcoming Limitations of Electrostatic Models by S. Manukhov, A. Kolesov , V. V. Palyulin and A. Korotin.
The repository contains reproducible PyTorch source code for computing maps for both noise-to-data and data-to-data scenarios in high dimensions with neural networks. Examples are provided for toy 3D, conditional and unconditional data generation and unpaired translation tasks.
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 may not work as intended in older/newer torch versions. Versions of other libraries are specified in requirements.txt.
All the experiments are issued in the form of pretty self-explanatory jupyter notebooks.
src- auxiliary source code for constructing the neural network model and preparing data.notebooks/TrainingToyExperiments.ipynb- the notebook of 3D illustrative examples.notebooks/IFMCelebaGeneration.ipynb- the notebook of unconditional generation with CelebA dataset.notebooks/IFMCIFAR10Generation.ipynb- the notebook of unconditional generation with CIFAR10 dataset.notebooks/IFMConditional.ipynb- the notebook of conditional generation with CIFAR10 dataset.notebooks/IFMSummer2Winter.ipynb- the notebook of unpaired translation from Summer to Winter landscapes.notebooks/IFMCMTranslation.ipynb- the notebook of unpaired translation from colored '2' to '3' MNIST digits.
 CIFAR-10 32x32 |
 CelebA 64x64 |
Image Generation: Samples obtained by IFM (ours) with the independent plan, electrostatic-based approaches EFM and PFGM & PFGM++, flow-based FM, diffusion-based DDPM and StyleGAN.
We also report quantitative results of IFM with FID metrics and compare with related works:
| Dataset | IFM (Ours) | EFM | PFGM++ | PFGM | FM | DDPM | StyleGAN |
|---|---|---|---|---|---|---|---|
| CIFAR-10 (32×32) | 2.28 | 2.62 | 2.15 | 2.76 | 2.99 | 3.12 | 2.48 |
| CelebA (64×64) | 3.07 | >100 | 2.89 | 3.95 | 14.45 | 12.26 | 3.68 |
Unconditional Image Generation: FID↓ on CIFAR-10 and CelebA for our IFM, EFM, PFGM++, FM, StyleGAN and DDPM.
(a) Colored digits '2' → '3' (b) Winter → Summer
Image Translation: Samples obtained by IFM (ours) with/without the minibatch plan, electrostatic-based approach EFM, flow-based FM, diffusion-based DDIB and adversarial CycleGAN.
We also report quantitative results of IFM with CMMD metrics and compare with related works:
| Dataset / Method | IFM-MB (our) | IFM (our) | EFM | FM | CycleGAN | DDIB |
|---|---|---|---|---|---|---|
| '2' → '3' (32×32) | 0.87 | 0.95 | 0.93 | 1.06 | 0.90 | 0.96 |
| W → S (64×64) | 1.13 | 1.25 | ≫1 | ≫1 | 1.33 | 1.39 |
Unpaired Image Translation: CMMD↓ on W→S and digits '2'→'3' for our IFM, EFM, FM, CycleGAN and DDIB.
pip install -r requirements.txt- Download datasets
- Set downloaded dataset in appropriate subfolder in
data/. - Run notebook with appropriate experiment.