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

arXiv: https://arxiv.org/abs/2505.08246 · HTML: https://mlsanity.com/paper/2505.08246/

## 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.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 20 of 20)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Generative Models as a Data Source for Multiview Representation Learning](https://mlsanity.com/paper/2106.05258/) (2021)
- [Detecting, Explaining, and Mitigating Memorization in Diffusion Models](https://mlsanity.com/paper/2407.21720/) (2024)
- [Score-based Diffusion Models in Function Space](https://mlsanity.com/paper/2302.07400/) (2023)
- [Neural Conservation Laws: A Divergence-Free Perspective](https://mlsanity.com/paper/2210.01741/) (2022)
- [A Reproducible Extraction of Training Images from Diffusion Models](https://mlsanity.com/paper/2305.08694/) (2023)
- [Analysis of p-Laplacian Regularization in Semi-Supervised Learning](https://mlsanity.com/paper/1707.06213/) (2017)
- [Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapes](https://mlsanity.com/paper/2412.04140/) (2024)
- [Manifold Induced Biases for Zero-shot and Few-shot Detection of Generated Images](https://mlsanity.com/paper/2504.15470/) (2025)
- [Spectral Decompositions using One-Homogeneous Functionals](https://mlsanity.com/paper/1601.02912/) (2016)
- [Spectral Total-Variation Processing of Shapes: Theory and Applications](https://mlsanity.com/paper/2209.07517/) (2022)
- [p-Laplacian Adaptation for Generative Pre-trained Vision-Language Models](https://mlsanity.com/paper/2312.10613/) (2023)

## 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.