Only 1 GPU is required.

IDFF is a novel generative modeling framework that simultaneously learns an implicit flow and a scoring model.
These components operate jointly during sampling, enabling fast, accurate generation across both images and time-series data.

Thanks to its momentum-driven structure, IDFF reduces the number of function evaluations (NFE) by more than 10× compared to traditional conditional flow matching (CFM) models.

• Combines score-based and flow-based generative models in a unified second-order SDE framework.
• Dynamically modulates sample generation with first- and second-order gradients, controlled by γ₁, γ₂, ...
• Supports both 2D synthetic distributions (e.g., checkerboard, spirals) and high-dimensional molecular dynamics (MD) data.
• Fast Inference: High-quality samples with as few as 2–3 function evaluations.
• Easy Integration: Compatible with torchdiffeq and torchsde solvers; plug in your own models.

We demonstrate the effect of IDFF on a synthetic 2D distribution using KDE overlays and trajectory visualization.

• Models tested:

  • Standard CFM
  • IDFF with various $(\gamma_1, \gamma_2)$ configurations

• Metric: Maximum Mean Discrepancy (MMD)

  • IDFF achieves lower MMD than CFM even with fewer NFEs

Run:

python 2D_examples/Autograd_example_order2.py

We apply IDFF to molecular dynamics simulations, specifically backbone dihedral trajectories from PolyALA molecular chains.

• Objective: Learn to generate dynamics of PolyALA molecular chain.
• Architecture: MLP-based embedding model trained with IDFF.
• Output: Generated trajectories, phase space plots, and metrics like RMSE, MAE, CC.

Train & Evaluate:

python timeseris_example/MD_simulation.py

-Example Phase Space Plot:

You can customize the following parameters:

• gamma1, gamma2: momentum modulation
• nfe: number of function evaluations

• torch, torchsde, torchdiffeq
• matplotlib, seaborn, scikit-learn
• scipy, pandas, numpy

Install dependencies:

pip install -r requirements.txt

If you find this work useful, please cite:

@misc{rezaei2025implicitdynamicalflowfusion,
      title={Implicit Dynamical Flow Fusion (IDFF) for Generative Modeling}, 
      author={Mohammad R. Rezaei and Milos R. Popovic and Milad Lankarany and Rahul G. Krishnan},
      year={2025},
      eprint={2409.14599},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2409.14599}, 
}

For questions, feel free to raise an issue.