# Detecting and Mitigating Memorization in Diffusion Models through Anisotropy of the Log-Probability

arXiv: https://arxiv.org/abs/2601.20642 · HTML: https://mlsanity.com/paper/2601.20642/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 33 of its 37 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Photorealistic Video Generation with Diffusion Models](https://mlsanity.com/paper/2312.06662/) (2023)
- [Understanding and Mitigating Copying in Diffusion Models](https://mlsanity.com/paper/2305.20086/) (2023)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [A Self-Supervised Descriptor for Image Copy Detection](https://mlsanity.com/paper/2202.10261/) (2022)
- [Detecting, Explaining, and Mitigating Memorization in Diffusion Models](https://mlsanity.com/paper/2407.21720/) (2024)
- [A Reproducible Extraction of Training Images from Diffusion Models](https://mlsanity.com/paper/2305.08694/) (2023)
- [Unveiling and Mitigating Memorization in Text-to-image Diffusion Models through Cross Attention](https://mlsanity.com/paper/2403.11052/) (2024)
- [Boosting Diffusion Models with Moving Average Sampling in Frequency Domain](https://mlsanity.com/paper/2403.17870/) (2024)
- [Prompt Stealing Attacks Against Text-to-Image Generation Models](https://mlsanity.com/paper/2302.09923/) (2023)
- [Towards Memorization-Free Diffusion Models](https://mlsanity.com/paper/2404.00922/) (2024)
- [A Geometric Framework for Understanding Memorization in Generative Models](https://mlsanity.com/paper/2411.00113/) (2024)
- [Classifier-Free Guidance inside the Attraction Basin May Cause Memorization](https://mlsanity.com/paper/2411.16738/) (2024)
- [Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapes](https://mlsanity.com/paper/2412.04140/) (2024)
- [Exploring Local Memorization in Diffusion Models via Bright Ending Attention](https://mlsanity.com/paper/2410.21665/) (2024)
- [Multi-conditioned Graph Diffusion for Neural Architecture Search](https://mlsanity.com/paper/2403.06020/) (2024)

## Built on by (most cited first, 2 of 2)

- [Prompt-Guided Image Editing with Masked Logit Nudging in Visual Autoregressive Models](https://mlsanity.com/paper/2604.14591/) (2026)
- [I2PRef: Image-Driven Point Completion with Iterative Refinement](https://mlsanity.com/paper/2605.26914/) (2026)

## Abstract (arXiv)

Diffusion-based image generative models produce high-fidelity images through iterative denoising but remain vulnerable to memorization, where they unintentionally reproduce exact copies or parts of training images. Recent memorization detection methods are primarily based on the norm of score difference as indicators of memorization. We prove that such norm-based metrics are mainly effective under the assumption of isotropic log-probability distributions, which generally holds at high or medium noise levels. In contrast, analyzing the anisotropic regime reveals that memorized samples exhibit strong angular alignment between the guidance vector and unconditional scores in the low-noise setting. Through these insights, we develop a memorization detection metric by integrating isotropic norm and anisotropic alignment. Our detection metric can be computed directly on pure noise inputs via two conditional and unconditional forward passes, eliminating the need for costly denoising steps. Detection experiments on Stable Diffusion v1.4 and v2 show that our metric outperforms existing denoising-free detection methods while being at least approximately 5x faster than the previous best approach. Finally, we demonstrate the effectiveness of our approach by utilizing a mitigation strategy that adapts memorized prompts based on our developed metric. The code is available at https://github.com/rohanasthana/memorization-anisotropy .