Fractional Brownian Motion-Based Inpainting

This repository provides implementations of diffusion-based inpainting methods for reconstructing incomplete Euclidean distance matrices (EDMs) of fractional Brownian motion (fBm), as presented at NeurIPS 2024. The proposed methods leverage the intrinsic memory properties of fBm to perform statistical imputation, outperforming standard bioinformatics techniques in applications such as chromosomal segment reconstruction.

Overview

Fractional Brownian motion (fBm) is a stochastic process with both randomness and long-range correlations. This project examines how diffusion models can effectively reconstruct missing data in corrupted fBm-derived EDMs. The framework is evaluated on synthetic and experimental datasets, including:

• A dataset of fBm-derived EDMs at various memory exponents (H values).
• Fluorescence In Situ Hybridization (FISH) microscopy data with missing chromosomal segment distances.

Features

• Implements multiple inpainting techniques, including:
  • DDNM-based inpainting, a generalization of DDRM, RePaint.
  • Optimization-based reconstruction methods.
• Provides scripts to generate and evaluate corrupted EDMs.
• Computes Frechet Inception Distance (FID) to assess the quality of reconstructions.

Workflow

1. Dataset Generation: Use generate_exact_distance_matrices.py to create fBm-derived EDMs.
2. Training: Train a diffusion model using train.py to generalize samples from fBm EDMs.
3. Testing Reconstruction: Generate corrupted EDMs using generate_corrupted_mask.py.
4. Baseline Comparison: Evaluate different reconstruction methods using:
   • reconstruct_database_search.py
   • reconstruct_fista.py
   • reconstruct_traj_optimization.py
   • reconstruct_nearest_neighbor.py
5. Main Reconstruction Method: Run reconstruct_inpainting.py to apply diffusion-based inpainting and compare results with baselines.

Citation

If you use this code in your research, please cite our work:

@inproceedings{lobashevfbm,
  title={fBm-Based Generative Inpainting for the Reconstruction of Chromosomal Distances},
  author={Lobashev, Alexander and Guskov, Dmitry and Polovnikov, Kirill},
  booktitle = {Machine Learning and the Physical Sciences Workshop at NeurIPS},
  year      = {2024},
  month     = {December},
address   = {Vancouver, Canada}
}

License

This project is licensed under the MIT License.