Abstract
Fractional Brownian trajectories (fBm) feature both randomness and strong scale-free correlations, challenging generative models to reproduce the intrinsic memory characterizing the underlying process. Here we test a diffusion probabilistic model on a specific dataset of corrupted images corresponding to incomplete Euclidean distance matrices of fBm at various memory exponents $H$. Our dataset implies uniqueness of the data imputation in the regime of low missing ratio, where the remaining partial graph is rigid, providing the ground truth for the inpainting. We find that the conditional diffusion generation stably reproduces the statistics of missing fBm-distributed distances for different values of $H$ exponent. Furthermore, while diffusion models have been recently shown to remember samples from the training database, we show that diffusion-based inpainting behaves qualitatively different from the database search with the increasing database size. Finally, we apply our fBm-trained diffusion model with $H=1/3$ for completion of chromosome distance matrices obtained in single-cell microscopy experiments, showing its superiority over the standard bioinformatics algorithms. Our source code is available on GitHub at this https URL.
Abstract (translated)
分式布朗轨迹（fBm）具有随机性和强标度无关性，挑战生成模型对底层过程的固有记忆特征进行还原。在这里，我们在具有不同记忆指数$H$的完整欧氏距离矩阵的污损图像的特定数据集上对扩散概率模型进行测试。我们的数据集表明，在残差比低的情况下，数据缺失的鲁棒性是唯一的，而剩余的离散图是刚性的，为修复提供真实值。我们发现，条件扩散生成稳定地还原了不同$H$值下污损fBm分布的统计量。此外，扩散模型最近已经被证明可以从训练数据库中记住样本，但我们发现，随着数据库大小的增加，基于扩散的修复表现出与数据库搜索 qualitatively different的行为。最后，我们将$H=\frac{1}{3}$应用于从单细胞显微镜实验中获得的染色体距离矩阵的修复，证明了其优越性 over 标准生物信息学算法。我们的源代码可在此https URL上获取。
URL
https://arxiv.org/abs/2404.07029
