# SAC-Copula: Quality-Preserving Watermarking for Diffusion Language Models via Smooth Correlated Gumbel Fields

arXiv: https://arxiv.org/abs/2608.20839 · HTML: https://mlsanity.com/paper/2608.20839/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Robustness, privacy and adversarial aspects, one of 14 directions in Diffusion models.
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Placed in

- Diffusion models / [Robustness, privacy and adversarial aspects](https://mlsanity.com/diffusion/robustness-privacy-and-adversarial-aspects/)
- LLM safety and security / [Watermarking generated content and models](https://mlsanity.com/safety/watermarking-generated-content-and-models/)

## Builds on (most cited first, 15 of 15)

- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [ELI5: Long Form Question Answering](https://mlsanity.com/paper/1907.09190/) (2019)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [Paraphrasing evades detectors of AI-generated text, but retrieval is an effective defense](https://mlsanity.com/paper/2303.13408/) (2023)
- [Robust Distortion-free Watermarks for Language Models](https://mlsanity.com/paper/2307.15593/) (2023)
- [Provable Robust Watermarking for AI-Generated Text](https://mlsanity.com/paper/2306.17439/) (2023)
- [Publicly-Detectable Watermarking for Language Models](https://mlsanity.com/paper/2310.18491/) (2023)
- [A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rules](https://mlsanity.com/paper/2404.01245/) (2024)
- [WaterMax: breaking the LLM watermark detectability-robustness-quality trade-off](https://mlsanity.com/paper/2403.04808/) (2024)
- [Theoretically Grounded Framework for LLM Watermarking: A Distribution-Adaptive Approach](https://mlsanity.com/paper/2410.02890/) (2024)
- [A Watermark for Order-Agnostic Language Models](https://mlsanity.com/paper/2410.13805/) (2024)
- [Non-Markovian Discrete Diffusion with Causal Language Models](https://mlsanity.com/paper/2502.09767/) (2025)
- [Watermarking Discrete Diffusion Language Models](https://mlsanity.com/paper/2511.02083/) (2025)
- [LR-DWM: Efficient Watermarking for Diffusion Language Models](https://mlsanity.com/paper/2601.12376/) (2026)
- [dgMARK: Decoding-Guided Watermarking for Diffusion Language Models](https://mlsanity.com/paper/2601.22985/) (2026)

## Built on by (most cited first, 1 of 1)

- [TANGO: Watermarking Masked Diffusion Language Models in Token Pairs](https://mlsanity.com/paper/2609.35224/) (2026)

## Abstract (arXiv)

Watermarking diffusion language models (DLMs) requires mechanisms compatible with iterative parallel unmasking rather than autoregressive decoding. Existing sampling-based watermarking methods typically inject position-wise i.i.d. perturbations, which can be poorly aligned with DLM decoding dynamics and degrade generation quality. We propose SAC-Copula, a quality-preserving watermarking method for DLMs based on smooth, locally correlated Gumbel perturbation fields constructed via a Gaussian copula. We further develop a SAC-aware detector using covariance-aware filtering and native-sample calibration. Mechanism-level analysis shows that local correlation reduces latent perturbation roughness and better matches iterative refinement dynamics. Experiments on LLaDA show that SAC-Copula achieves a favorable quality-detectability trade-off compared with existing baselines. In particular, further evaluations on Dream-7B and additional datasets show that SAC-Copula substantially improves PPL tail stability over the i.i.d. Gumbel baseline, while maintaining strong low-FPR detectability and competitive overall generation quality. Additional token-edit stress tests further assess watermark robustness under controlled synchronization drift. Code is available at https://github.com/PunkyKnife/SAC-Copula.