# Characterizing Memorization in Diffusion Language Models: Generalized Extraction and Sampling Effects

arXiv: https://arxiv.org/abs/2603.02333 · HTML: https://mlsanity.com/paper/2603.02333/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 32 of its 41 references that are in the map.
- First posted on arXiv 2 Mar 2026.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [Analyzing Leakage of Personally Identifiable Information in Language Models](https://mlsanity.com/paper/2302.00539/) (2023)
- [Are Large Pre-Trained Language Models Leaking Your Personal Information?](https://mlsanity.com/paper/2205.12628/) (2022)
- [Scaling up Masked Diffusion Models on Text](https://mlsanity.com/paper/2410.18514/) (2024)
- [LLaDA2.0: Scaling Up Diffusion Language Models to 100B](https://mlsanity.com/paper/2512.15745/) (2025)
- [ProPILE: Probing Privacy Leakage in Large Language Models](https://mlsanity.com/paper/2307.01881/) (2023)
- [PLANNER: Generating Diversified Paragraph via Latent Language Diffusion Model](https://mlsanity.com/paper/2306.02531/) (2023)
- [Demystifying Verbatim Memorization in Large Language Models](https://mlsanity.com/paper/2407.17817/) (2024)
- [Measuring memorization in language models via probabilistic extraction](https://mlsanity.com/paper/2410.19482/) (2024)
- [Extracting memorized pieces of (copyrighted) books from open-weight language models](https://mlsanity.com/paper/2505.12546/) (2025)
- [Extracting books from production language models](https://mlsanity.com/paper/2601.02671/) (2026)
- [ROME: Memorization Insights from Text, Logits and Representation](https://mlsanity.com/paper/2403.00510/) (2024)
- [Trustworthy Machine Learning via Memorization and the Granular Long-Tail: A Survey on Interactions, Tradeoffs, and Beyond](https://mlsanity.com/paper/2503.07501/) (2025)

## Built on by (most cited first, 3 of 3)

- [The Safety-Aware Denoiser for Text Diffusion Models](https://mlsanity.com/paper/2605.08116/) (2026)
- [Extracting Training Data from Diffusion Language Models via Infilling](https://mlsanity.com/paper/2605.24173/) (2026)
- [Conditional Generation of Creative Chess Puzzles with Diffusion Models](https://mlsanity.com/paper/2609.38577/) (2026)

## Abstract (arXiv)

Autoregressive language models (ARMs) have been shown to memorize and occasionally reproduce training data verbatim, raising concerns about privacy and copyright liability. Diffusion language models (DLMs) have recently emerged as a competitive alternative, yet their memorization behavior remains largely unexplored due to fundamental differences in generation dynamics. To address this gap, we present a systematic theoretical and empirical characterization of memorization in DLMs. We propose a generalized probabilistic extraction framework that unifies prefix-conditioned decoding and diffusion-based generation under arbitrary masking patterns and stochastic sampling trajectories. Theorem 4.3 establishes a monotonic relationship between sampling resolution and memorization: increasing resolution strictly increases the probability of exact training data extraction, implying that autoregressive decoding corresponds to a limiting case of diffusion-based generation by setting the sampling resolution maximal. Extensive experiments across model scales and sampling strategies validate our theoretical predictions. Under aligned prefix-conditioned evaluations, we further demonstrate that DLMs exhibit substantially lower memorization-based leakage of personally identifiable information (PII) compared to ARMs.