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

Snigdha Chandan Khilar

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 3 functions out of this paper's own repositories and ran 3 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

Repositories linked to this paper

• nssprogrammer/pflow

Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.

Abstract

Current topology-aware diffusion models suffer from a fundamental architectural mismatch: they corrupt inputs with topology-agnostic Gaussian noise but attempt to recover structural features via conditional side channels in the reverse network. To resolve this, the authors introduce PFlow-T, a novel generative model that defines its forward diffusion process entirely through the persistent homology of the data. In PFlow-T, the time parameter does not track Gaussian noise injection; instead, it measures the fraction of H 1 persistence-mass that has been destroyed. The forward operator systematically eliminates H 1 topological features (such as holes) in strict ascending order of their persistence. Because the corruption is topologically structured, the reverse network learns to directly invert it to predict the clean state (x 0 ) in a single inference step, rather than retrieving topology from external conditioning. Empirical evaluations on MNIST digits ({0, 1, 8}) demonstrate that PFlow-T drastically outperforms a parameter-matched DDPM baseline conditioned on a 64-d persistence landscape. PFlow-T successfully honors the requested Betti numbers (β 1 ∈ {0, 1, 2}) in 99.6%, 96.0%, and 84.8% of generations, compared to the baseline's 96.4%, 3.2%, and 0.0% (an average gap of 88.8 percentage points for β 1 ≥ 1). Furthermore, on out-of-distribution conditioning tasks-where the model must generate a topology contradicting the digit's class prior-PFlow-T succeeds in 92.0% of cases versus the baseline's 9.7%. PFlow-T stands as the first generative architecture where persistent homology acts as the core substrate of the forward process. The authors acknowledge current scope limitations, noting that the forward operator is a pixel-space proxy for exact Edelsbrunner-Harer pair cancellation and is tested at low resolutions, leaving a faithful persistence-module state space for future work.

For agents

The same record, over MCP at https://syntology.ai/mcp:

get_harvested_code_for_paper("2605.17555")
get_code_for_paper("2605.17555")
have("2605.17555")

Connect an agent — have() is free.