PFlow-T: A Persistence-Driven Forward Process for Topology-Controlled Generation

TL;DR

PFlow-T introduces a novel generative model that uses persistent homology to guide the forward process, improving topology-aware generation especially for low-resolution images.

Contribution

It is the first generative architecture to employ persistent homology in the forward process, addressing architectural mismatches in topology-aware diffusion models.

Findings

Outperforms baseline models in generating requested Betti numbers

Effectively handles out-of-distribution tasks

Successfully applied to MNIST digits zero, one, and eight

Abstract

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