# Sequential Diffusion Language Models

arXiv: https://arxiv.org/abs/2509.24007 · HTML: https://mlsanity.com/paper/2509.24007/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 43 of its 52 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 30 of 43)

- [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)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [Better & Faster Large Language Models via Multi-token Prediction](https://mlsanity.com/paper/2404.19737/) (2024)
- [Blockwise Parallel Decoding for Deep Autoregressive Models](https://mlsanity.com/paper/1811.03115/) (2018)
- [Scaling Diffusion Language Models via Adaptation from Autoregressive Models](https://mlsanity.com/paper/2410.17891/) (2024)

## Built on by (most cited first, 19 of 19)

- [WeDLM: Reconciling Diffusion Language Models with Standard Causal Attention for Fast Inference](https://mlsanity.com/paper/2512.22737/) (2025)
- [TiDAR: Think in Diffusion, Talk in Autoregression](https://mlsanity.com/paper/2511.08923/) (2025)
- [LocateAnything: Fast and High-Quality Vision-Language Grounding with Parallel Box Decoding](https://mlsanity.com/paper/2605.27365/) (2026)
- [CoDAR: Continuous Diffusion Language Models are More Powerful Than You Think](https://mlsanity.com/paper/2603.02547/) (2026)
- [Stable-DiffCoder: Pushing the Frontier of Code Diffusion Large Language Model](https://mlsanity.com/paper/2601.15892/) (2026)
- [Deferred Commitment Decoding for Diffusion Language Models](https://mlsanity.com/paper/2601.02076/) (2026)
- [DiffusionVL: Translating Any Autoregressive Models into Diffusion Vision Language Models](https://mlsanity.com/paper/2512.15713/) (2025)
- [Dataset-Level Metrics Attenuate Non-Determinism: A Fine-Grained Non-Determinism Evaluation in Diffusion Language Models](https://mlsanity.com/paper/2604.13413/) (2026)
- [Towards A Generative Protein Evolution Machine with DPLM-Evo](https://mlsanity.com/paper/2605.00182/) (2026)
- [Window-Diffusion: Accelerating Diffusion Language Model Inference with Windowed Token Pruning and Caching](https://mlsanity.com/paper/2601.20332/) (2026)
- [Diffusion Language Models: An Experimental Analysis](https://mlsanity.com/paper/2606.19475/) (2026)
- [Set Diffusion: Interpolating Token Orderings Between Autoregression and Diffusion for Fast and Flexible Decoding](https://mlsanity.com/paper/2607.01775/) (2026)
- [Fast SceneScript: Fast and Accurate Language-Based 3D Scene Understanding via Multi-Token Prediction](https://mlsanity.com/paper/2512.05597/) (2025)
- [Reinforced Fast Weights with Next-Sequence Prediction](https://mlsanity.com/paper/2602.16704/) (2026)
- [Differences in Text Generated by Diffusion and Autoregressive Language Models](https://mlsanity.com/paper/2605.12522/) (2026)
- [Bifocal Diffusion Language Models: Asymmetric Bidirectional Context for Parallel Generation](https://mlsanity.com/paper/2606.27732/) (2026)
- [Locate Anything in Videos: Rethinking Efficient Generative Spatio-Temporal Video Grounding](https://mlsanity.com/paper/2608.28192/) (2026)
- [d-OPD: Future-Aware On-Policy Distillation for Block Diffusion Language Models](https://mlsanity.com/paper/2609.35362/) (2026)
- [HyperZip: Efficient Data Compression through Personalized Diffusion LLMs with Hypernetworks](https://mlsanity.com/paper/2609.36357/) (2026)

## Abstract (arXiv)

Diffusion language models (DLMs) have strong theoretical efficiency but are limited by fixed-length decoding and incompatibility with key-value (KV) caches. Block diffusion mitigates these issues, yet still enforces a fixed block size and requires expensive training. We introduce Next Sequence Prediction (NSP), which unifies next-token and next-block prediction, enabling the model to adaptively determine the generation length at each step. When the length is fixed to 1, NSP reduces to standard next-token prediction. Building on NSP, we propose Sequential Diffusion Language Model (SDLM), which can retrofit pre-trained autoregressive language models (ALMs) at minimal cost. Specifically, SDLM performs diffusion inference within fixed-size mask blocks, but dynamically decodes consecutive subsequences based on model confidence, thereby preserving KV-cache compatibility and improving robustness to varying uncertainty and semantics across the sequence. Experiments show that SDLM matches or surpasses strong autoregressive baselines using only 3.5M training samples, while achieving 2.1 higher throughput than Qwen-2.5. Notably, the SDLM-32B model delivers even more pronounced efficiency gains, demonstrating the strong scalability potential of our modeling paradigm. Project page and codes: https://github.com/OpenGVLab/SDLM