# BlockGen: Flexible Blockwise Sequence Modeling with Hybrid Samplers

arXiv: https://arxiv.org/abs/2606.02241 · HTML: https://mlsanity.com/paper/2606.02241/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 42 of its 61 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Placed in

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

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [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)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [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)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [One Billion Word Benchmark for Measuring Progress in Statistical Language Modeling](https://mlsanity.com/paper/1312.3005/) (2013)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [DiffusionBERT: Improving Generative Masked Language Models with Diffusion Models](https://mlsanity.com/paper/2211.15029/) (2022)
- [SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control](https://mlsanity.com/paper/2210.17432/) (2022)
- [Remasking Discrete Diffusion Models with Inference-Time Scaling](https://mlsanity.com/paper/2503.00307/) (2025)
- [Flex Attention: A Programming Model for Generating Optimized Attention Kernels](https://mlsanity.com/paper/2412.05496/) (2024)
- [Simple Guidance Mechanisms for Discrete Diffusion Models](https://mlsanity.com/paper/2412.10193/) (2024)
- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [Diffusion LLMs Can Do Faster-Than-AR Inference via Discrete Diffusion Forcing](https://mlsanity.com/paper/2508.09192/) (2025)
- [Accelerating Diffusion LLMs via Adaptive Parallel Decoding](https://mlsanity.com/paper/2506.00413/) (2025)
- [Energy-Based Diffusion Language Models for Text Generation](https://mlsanity.com/paper/2410.21357/) (2024)
- [Path Planning for Masked Diffusion Model Sampling](https://mlsanity.com/paper/2502.03540/) (2025)
- [A Deep and Tractable Density Estimator](https://mlsanity.com/paper/1310.1757/) (2013)
- [Training and Inference on Any-Order Autoregressive Models the Right Way](https://mlsanity.com/paper/2205.13554/) (2022)
- [Think While You Generate: Discrete Diffusion with Planned Denoising](https://mlsanity.com/paper/2410.06264/) (2024)
- [Informed Correctors for Discrete Diffusion Models](https://mlsanity.com/paper/2407.21243/) (2024)
- [Any-Order Flexible Length Masked Diffusion](https://mlsanity.com/paper/2509.01025/) (2025)
- [Theoretical Benefit and Limitation of Diffusion Language Model](https://mlsanity.com/paper/2502.09622/) (2025)
- [Fine-Tuning Masked Diffusion for Provable Self-Correction](https://mlsanity.com/paper/2510.01384/) (2025)
- [TiDAR: Think in Diffusion, Talk in Autoregression](https://mlsanity.com/paper/2511.08923/) (2025)

## Abstract (arXiv)

Is the uniform-state diffusion framework a more powerful paradigm for discrete diffusion? Recent studies indicate that this may be the case. In combination with predictor-corrector samplers, uniform-state diffusion models (USDMs) produce samples of higher-quality than masked diffusion models (MDMs), and USDMs equal or outperform MDMs in downstream tasks, even though they exhibit greater perplexity. Two issues remain unresolved. First, existing work compares uniform and masked diffusion with un-informed correctors that re-inject noise at random positions, rather than targeting tokens most likely to be wrong. Second, prior work compares full-sequence diffusion models, so we do not know whether the same conclusion holds when tokens are generated block by block. To address these issues, we introduce BlockGen, a blockwise sequence model that we instantiate with both masked and uniform diffusion. BlockGen trains on a mixture of block sizes and its likelihood interpolates between AR and pure diffusion more finely than models with a fixed block size. BlockGen enables AR-informed predictor-corrector sampling (ARPC), which combines AR and diffusion predictions to re-generate unlikely tokens without an auxiliary verifier. Under ancestral sampling, uniform outperforms masked in the block-by-block setting, especially in the few-step regime. Under ARPC, the gap closes and reverses at high NFE. With block size 16 on GSM8K, MDMs reach slightly higher accuracy than USDMs, and we observe a similar trend in Generative Perplexity on OpenWebText. Find our code at https://github.com/jdeschena/blockgen.