# Fixed State, Long Reach: What a Constant-Size Cache Buys Block Diffusion at Scale

arXiv: https://arxiv.org/abs/2609.11998 · HTML: https://mlsanity.com/paper/2609.11998/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 40 of its 41 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)
- State-space sequence models (S4, Mamba) / [Core SSM architectures for language](https://mlsanity.com/ssm/core-ssm-architectures-for-language/)

## Builds on (most cited first, 30 of 40)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [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)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [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)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Models](https://mlsanity.com/paper/2402.19427/) (2024)
- [An Empirical Study of Mamba-based Language Models](https://mlsanity.com/paper/2406.07887/) (2024)
- [Samba: Simple Hybrid State Space Models for Efficient Unlimited Context Language Modeling](https://mlsanity.com/paper/2406.07522/) (2024)
- [dLLM-Cache: Accelerating Diffusion Large Language Models with Adaptive Caching](https://mlsanity.com/paper/2506.06295/) (2025)
- [Nemotron-CC: Transforming Common Crawl into a Refined Long-Horizon Pretraining Dataset](https://mlsanity.com/paper/2412.02595/) (2024)
- [dKV-Cache: The Cache for Diffusion Language Models](https://mlsanity.com/paper/2505.15781/) (2025)
- [Fast-dLLM v2: Efficient Block-Diffusion LLM](https://mlsanity.com/paper/2509.26328/) (2025)
- [The Diffusion Duality](https://mlsanity.com/paper/2506.10892/) (2025)

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

- [d-OPD: Future-Aware On-Policy Distillation for Block Diffusion Language Models](https://mlsanity.com/paper/2609.35362/) (2026)
- [RL Post-Training Diffusion Language Models Along Their Own Generation Paths](https://mlsanity.com/paper/2610.17266/) (2026)

## Abstract (arXiv)

Diffusion language models decode tokens in parallel, but their bidirectional denoiser rules out the naive key--value (KV) cache behind fast autoregressive inference. Block diffusion restores caching by decoding block-by-block, and the block caches deployed on it so far are tied to attention: O(L)in memory and, if used as training-free retrofits, only an approximation of the model's computation. Both constraints can be overcome: sequence mixers that summarize finalized blocks into a reusable state support block caching, and the corresponding block-causal training objective makes the cache exact. We study this recipe at scale, pretraining three 3B block-diffusion denoisers (attention, mamba, and hybrid) on 300B tokens under one single-frontier objective and decoding all three through a single cached interface. Only the state-space cache is O(1) in sequence length: its memory and per-step latency stay constant at any context length, while an attention cache remains O(L). At 256k tokens (where attention has grown to 82GB and 29 ms/step), the Mamba cache delivers 4.3x lower latency, 11x less memory, and 2.6x higher single-stream throughput; and because that footprint is constant it scales with batch as well, reaching 14x the aggregate throughput, where attention cannot run beyond a single stream. The same linear-state bias lets the Mamba and hybrid backbones keep retrieving out to 8-16x their training length, whereas attention's retrieval collapses at 2x, at no measured quality cost.