mlsanityData to 14 Oct 2026

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

arXiv 2605.17555 ↗First posted 17 May 2026cs.LG cs.CVcited by 0

On the map: Diffusion models → Flow matching, time series and science

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

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.

Builds on

15 of 30 references.

Closest ancestors · 1

Same direction, newest first

  1. 2024TopoDiffusionNet: A Topology-aware Diffusion Model22 Oct

Other references · 14

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
  6. 2019Topological Autoencoderscited by 127
  7. 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 126
  8. 2017Deep Learning with Topological Signaturescited by 114
  9. 2022Poisson Flow Generative Modelscited by 95
  10. 2021Topological Graph Neural Networkscited by 87
  11. 2019A Topology Layer for Machine Learningcited by 80
  12. 2019A Framework for Differential Calculus on Persistence Barcodescited by 29
2 more
  1. 2023GenPhys: From Physical Processes to Generative Modelscited by 19
  2. 2024Topology-Aware Latent Diffusion for 3D Shape Generationcited by 13

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Close in wording, no citation either way

  1. 2026PolyFlow: Continuous Topology Embedding Flow Matching for Artist-style Mesh Generation
  2. 2025CoPHo: Classifier-guided Conditional Topology Generation with Persistent Homology
  3. 2026Topological Flow Matching
  4. 2026Stochastic Dynamics on Persistence Diagram Space via Reinforcement Learning
  5. 2025Topology Guidance: Controlling the Outputs of Generative Models via Vector Field Topology
  6. 2025Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions
  7. 2026AoiZora: Topology-Aware Auto-Parallel Optimization for Inference of Diffusion Transformers
  8. 2025Efficiency vs. Fidelity: A Comparative Analysis of Diffusion Probabilistic Models and Flow Matching on Low-Resource Hardware