用神经隐式函数建模稀疏观测的多变量随机场，生成逼真结果并保留不确定性。
Random Process Flow Matching: Generative Implicit Representations of Multivariate Random Fields
- 将向量场建为神经隐式函数，结合随机傅里叶特征实现任意位置查询。
- 在高频、高稀疏或高维条件下仍生成真实样本且不确定性校准良好。
- 适合数据稀缺场景下的重建任务，尤其需要可追溯不确定性的应用。
生成模型为学习数据分布提供了强大框架。早期方法依赖高斯过程（GP）进行不确定性感知预测，后转向更大可训练模型以捕捉更复杂分布。本文提出随机过程流（RP Flow），一种基于流匹配的框架，将向量场表示为神经隐式函数。与现代生成方法不同，本框架仅依赖单个观测场，且仅能获取稀疏测量。RP Flow利用随机傅里叶特征学习隐式信号表示，可在有限观测下任意位置查询，同时通过集成采样编码不确定性。我们通过源空间中的GP回归构建贝叶斯后验，生成高质量样本。实验表明，该框架即使在高频率、高稀疏度或高维度等挑战性条件下，仍能生成逼真样本并提供校准的不确定性估计。这些成果标志着生成模型在数据稀缺且需追踪不确定性的重建任务中迈出了重要一步。
原文摘要 · Abstract (English)
Generative modeling provides a powerful framework for learning data distributions. These models initially relied on probabilistic methods such as Gaussian Processes (GP) for uncertainty-aware predictions and shifted towards larger trainable models to learn more complex distributions. In this work, we introduce Random Process (RP) Flow, a Flow Matching-based framework that represents the vector field as a neural implicit function. Unlike modern generative methods, our setting involves a single observed field, from which only sparse measurements are available. RP Flow uses Random Fourier Features to learn an implicit signal representation that can be queried at any arbitrary location from a limited set of observations, while encoding uncertainty through ensemble sampling. We propose constructing a Bayesian posterior by GP regression in the source space to generate high-quality samples. Our empirical results demonstrate that this framework generates realistic samples along with calibrated uncertainty estimates, even under challenging conditions such as high frequency, high sparsity, or high dimensionality. These findings position RP Flow as a milestone towards generative models for reconstruction tasks where data is scarce and uncertainty must remain traceable.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。