mlsanityData to 14 Oct 2026

The Geometry of Memorization: Finite-Time Spectral Sensitivity as a Diagnostic for Flow Matching Models

arXiv 2607.12616 ↗First posted 14 Jul 2026cs.LGcited by 0

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

Abstract (arXiv)

Continuous-time generative frameworks construct probability paths between base and target domains by optimizing time-dependent velocity fields. While theoretical targets favor straight trajectories, empirical networks develop complex path deformations. This paper presents the Finite-Time Spectral Sensitivity (FTSS) g(t), a gradient-free, forward-pass metric that exposes flow geometry by tracking the root-mean-square singular value of the state-transition matrix. Serving as a continuous proxy for stable rank, g(t) reveals a distinct geometric pathology under data scarcity: while generalizing models maintain stable effective dimensions, overfitting causes a spectral collapse. We leverage this structural phenomenon to develop an internal geometric audit based on g(t). Our framework detects generative memorization using purely internal trajectory dynamics, removing the need for external membership queries or baseline data comparison.

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 12 of its 18 references that are in the map. First posted on arXiv 14 Jul 2026.

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12 of 18 references.

Closest ancestors · 2

Same direction, newest first

  1. 2022Flow Matching for Generative Modeling6 Oct
  2. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 10

  1. 2022Scalable Diffusion Models with Transformerscited by 6,054
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2016Membership Inference Attacks against Machine Learning Modelscited by 2,281
  4. 2016Density estimation using Real NVPcited by 2,042
  5. 2023Extracting Training Data from Diffusion Modelscited by 732
  6. 2017Spectrally-normalized margin bounds for neural networkscited by 686
  7. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 594
  8. 2020What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimationcited by 497
  9. 2022Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Modelscited by 424
  10. 2018Sensitivity and Generalization in Neural Networks: an Empirical Studycited by 189

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  4. 2026Particle Dynamics of Flow Matching and Classifier-Free Guidance from a Stagewise Geometry Perspective
  5. 2025Latent Iterative Refinement Flow: A Geometric Constrained Approach for Few-Shot Generation
  6. 2026Manifold-Stable Flow Matching
  7. 2026Geometry-Aware Time Reparameterization for Flow-Map Distillation
  8. 2024Losing dimensions: Geometric memorization in generative diffusion