用分数布朗运动建模时间记忆，提升蛋白质结构与图像转换的预测精度。
Fractional Diffusion Bridge Models
- 基于分数布朗运动的近似马尔可夫模型，保留长期依赖特性。
- 在蛋白质构象预测中，原子位置均方根偏差降低，图像转换FID更优。
- 适用于有时间相关性的生成建模，如生物结构与跨域图像生成。
我们提出分数扩散桥模型（FDBM），一种由分数布朗运动（fBM）近似驱动的新型生成扩散桥框架。真实随机过程具有记忆效应、长程依赖、粗糙性及异常扩散等特征，传统基于布朗运动（BM）的模型无法捕捉这些特性。为此，我们采用近期提出的fBM马尔可夫近似（MA-fBM），构建了可进行有效推断同时保持非马尔可夫特性的FDBM。我们证明了耦合保持的生成扩散桥的存在性，并用于从配对训练数据中预测未来状态。进一步将该框架拓展至薛定谔桥问题，推导出一种合理的损失函数以学习无配对数据间的映射。我们在两类任务上评估：基于对齐数据的蛋白质构象未来预测，以及无配对图像转换。在两项任务中，相比布朗运动基线，FDBM均表现更优，蛋白质结构预测中Cα原子位置的均方根偏差（RMSD）更低，图像转换中弗雷歇起始距离（FID）更小。
原文摘要 · Abstract (English)
We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of memory effects (correlations in time), long-range dependencies, roughness and anomalous diffusion phenomena that are not captured in standard diffusion or bridge modeling due to the use of Brownian motion (BM). As a remedy, leveraging a recent Markovian approximation of fBM (MA-fBM), we construct FDBM that enable tractable inference while preserving the non-Markovian nature of fBM. We prove the existence of a coupling-preserving generative diffusion bridge and leverage it for future state prediction from paired training data. We then extend our formulation to the Schrödinger bridge problem and derive a principled loss function to learn the unpaired data translation. We evaluate FDBM on both tasks: predicting future protein conformations from aligned data, and unpaired image translation. In both settings, FDBM achieves superior performance compared to the Brownian baselines, yielding lower root mean squared deviation (RMSD) of C$_α$ atomic positions in protein structure prediction and lower Fréchet Inception Distance (FID) in unpaired image translation.
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