mlsanityData to 14 Oct 2026

Identifying Memorization of Diffusion Models through p-Laplace Analysis: Estimators, Bounds and Applications

arXiv 2505.08246 ↗First posted 13 May 2025cs.CV cs.NA math.NAcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models, today's leading image generative models, estimate the score function, i.e. the gradient of the log probability of (perturbed) data samples, without direct access to the underlying probability distribution. This work investigates whether the estimated score function can be leveraged to compute higher-order differentials, namely the p-Laplace operators. We show that these operators can be employed to identify memorized training data. We propose a numerical p-Laplace approximation based on the learned score functions, showing its effectiveness in identifying key features of the probability landscape. Furthermore, theoretical error-bounds to these estimators are proven and demonstrated numerically. We analyze the structured case of Gaussian mixture models, and demonstrate that the results carry-over to text-conditioned image generative models (text-to-image), where memorization identification based on the p-Laplace operator is performed for the first time, showing its advantage on 500 memorized prompts (~3000 generated images) in a post-generation regime, especially when the conditioning text is unavailable.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 20 of its 78 references that are in the map. First posted on arXiv 13 May 2025.

Builds on

20 of 78 references.

Closest ancestors · 6

Same direction, newest first

  1. 2024Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapes5 Dec
  2. 2024Detecting, Explaining, and Mitigating Memorization in Diffusion Models31 Jul
  3. 2023Generalization in diffusion models arises from geometry-adaptive harmonic representations4 Oct
  4. 2023Score-based Diffusion Models in Function Space14 Feb
  5. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  6. 2021Improved Denoising Diffusion Probabilistic Models18 Feb

Other references · 14

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  2. 2023Extracting Training Data from Diffusion Modelscited by 732
  3. 2020What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimationcited by 497
  4. 2019Does Learning Require Memorization? A Short Tale about a Long Tailcited by 460
  5. 2022Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Modelscited by 424
  6. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 148
  7. 2021Generative Models as a Data Source for Multiview Representation Learningcited by 104
  8. 2022Neural Conservation Laws: A Divergence-Free Perspectivecited by 70
  9. 2023A Reproducible Extraction of Training Images from Diffusion Modelscited by 61
  10. 2017Analysis of p-Laplacian Regularization in Semi-Supervised Learningcited by 39
  11. 2025Manifold Induced Biases for Zero-shot and Few-shot Detection of Generated Imagescited by 10
  12. 2016Spectral Decompositions using One-Homogeneous Functionalscited by 7
2 more
  1. 2022Spectral Total-Variation Processing of Shapes: Theory and Applicationscited by 2
  2. 2023p-Laplacian Adaptation for Generative Pre-trained Vision-Language Modelscited by 1

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  1. 2025Memorization and Regularization in Generative Diffusion Models
  2. 2023On Memorization in Diffusion Models
  3. 2025How Diffusion Models Memorize
  4. 2025Provable Separations between Memorization and Generalization in Diffusion Models
  5. 2025Quantifying the Ease of Reproducing Training Data in Unconditional Diffusion Models
  6. 2026First Learn, Then Memorize: The Spectral Bias of Diffusion Models
  7. 2025On the Edge of Memorization in Diffusion Models
  8. 2026Loss Curvature as a Sampling-Free Proxy for Memorization in Diffusion Models