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

arXiv: https://arxiv.org/abs/2605.17555 · HTML: https://mlsanity.com/paper/2605.17555/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 17 May 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)
- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [A Framework for Differential Calculus on Persistence Barcodes](https://mlsanity.com/paper/1910.00960/) (2019)
- [GenPhys: From Physical Processes to Generative Models](https://mlsanity.com/paper/2304.02637/) (2023)
- [Topology-Aware Latent Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2401.17603/) (2024)
- [TopoDiffusionNet: A Topology-aware Diffusion Model](https://mlsanity.com/paper/2410.16646/) (2024)

## Abstract (arXiv)

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