用拓扑持久性设计生成过程，精准控制图像孔洞结构。
PFlow-T: A Persistence-Driven Forward Process for Topology-Controlled Generation
- 前向过程基于持久同调，按拓扑特征持久性逐步破坏
- 生成结果在贝蒂数控制上显著优于基线模型
- 适合需要精确拓扑结构控制的生成任务
当前拓扑感知扩散模型存在架构不匹配问题：前向过程使用高斯噪声破坏数据，却通过条件侧通道恢复结构特征。为此，我们提出PFlow-T，一种完全基于持久同调构建前向过程的生成模型。在该模型中，时间衡量的是H1拓扑特征（如孔洞）的消失程度，而非高斯噪声注入；特征的消除依据其持久性。反向网络直接逆向这一结构化破坏，在一步内预测出干净状态。在MNIST数字0、1、8上的测试表明，PFlow-T在生成指定贝蒂数和处理分布外任务时显著优于基线模型。PFlow-T是首个将持久同调用于前向过程的生成架构，但目前仅适用于低分辨率像素空间代理。
原文摘要 · Abstract (English)
Current topology aware diffusion models face an architectural mismatch by using Gaussian noise for corruption while recovering structural features through conditional side channels To fix this we introduce PFlow T a generative model that bases its forward process entirely on persistent homology In PFlow T time measures the destruction of H1 topological features like holes rather than Gaussian noise injection This forward process eliminates features based on their persistence The reverse network then directly inverts this structured corruption to predict the clean state in one step Tests on MNIST digits zero one and eight show PFlow T significantly outperforms a baseline model in generating requested Betti numbers and handling out of distribution tasks PFlow T is the first generative architecture using persistent homology for the forward process although we note it is currently limited to low resolution pixel space proxies
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