# Confidence-Based Decoding is Provably Efficient for Diffusion Language Models

arXiv: https://arxiv.org/abs/2603.22248 · HTML: https://mlsanity.com/paper/2603.22248/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 70 of its 76 references that are in the map.
- First posted on arXiv 23 Mar 2026.

## Placed in

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

## Builds on (most cited first, 30 of 70)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (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)
- [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)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [Scaling Diffusion Language Models via Adaptation from Autoregressive Models](https://mlsanity.com/paper/2410.17891/) (2024)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Mercury: Ultra-Fast Language Models Based on Diffusion](https://mlsanity.com/paper/2506.17298/) (2025)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Sampling](https://mlsanity.com/paper/2409.02908/) (2024)
- [Remasking Discrete Diffusion Models with Inference-Time Scaling](https://mlsanity.com/paper/2503.00307/) (2025)
- [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022)
- [Seed Diffusion: A Large-Scale Diffusion Language Model with High-Speed Inference](https://mlsanity.com/paper/2508.02193/) (2025)
- [Convergence for score-based generative modeling with polynomial complexity](https://mlsanity.com/paper/2206.06227/) (2022)
- [Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data](https://mlsanity.com/paper/2302.07194/) (2023)
- [LLaDA2.0: Scaling Up Diffusion Language Models to 100B](https://mlsanity.com/paper/2512.15745/) (2025)
- [Diffusion Models are Minimax Optimal Distribution Estimators](https://mlsanity.com/paper/2303.01861/) (2023)
- [A Reparameterized Discrete Diffusion Model for Text Generation](https://mlsanity.com/paper/2302.05737/) (2023)
- [LLaDA-V: Large Language Diffusion Models with Visual Instruction Tuning](https://mlsanity.com/paper/2505.16933/) (2025)
- [Accelerated Sampling from Masked Diffusion Models via Entropy Bounded Unmasking](https://mlsanity.com/paper/2505.24857/) (2025)
- [Dimple: Discrete Diffusion Multimodal Large Language Model with Parallel Decoding](https://mlsanity.com/paper/2505.16990/) (2025)
- [Path Planning for Masked Diffusion Model Sampling](https://mlsanity.com/paper/2502.03540/) (2025)

## Built on by (most cited first, 18 of 18)

- [Discrete-WAM: Unified Discrete Vision-Action Token Editing for World-Policy Learning](https://mlsanity.com/paper/2606.05645/) (2026)
- [Provably adaptive sampling with uniform and remasking discrete diffusion models](https://mlsanity.com/paper/2608.23554/) (2026)
- [DPRM: A Plug-in Doob h transform-induced Token-Ordering Module for Discrete Diffusion Models](https://mlsanity.com/paper/2604.24357/) (2026)
- [Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions](https://mlsanity.com/paper/2605.30153/) (2026)
- [Neither Parallel Nor Sequential: How DiffusionGemma Actually Commits Tokens](https://mlsanity.com/paper/2606.14620/) (2026)
- [ConvergeFlow: Language Flow with Provable Convergence to Token Embeddings](https://mlsanity.com/paper/2608.23551/) (2026)
- [The Confidence Shortcut: A Reasoning Failure Mode of Masked Diffusion Models](https://mlsanity.com/paper/2605.29123/) (2026)
- [Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices](https://mlsanity.com/paper/2606.23627/) (2026)
- [Conditional Total Correlation and the Serial Depth of Adaptive Parallel Sampling](https://mlsanity.com/paper/2608.25505/) (2026)
- [Focus on the Core: Empowering Diffusion Large Language Models by Self-Contrast](https://mlsanity.com/paper/2605.01373/) (2026)
- [Escaping Confidence Trap: Evolutionary Decoding for Mathematical Reasoning in Diffusion LLMs](https://mlsanity.com/paper/2608.00605/) (2026)
- [Schedule optimization for tau-leaping in masked discrete diffusion](https://mlsanity.com/paper/2609.21960/) (2026)
- [Entropy Can Flow, or It Can Guide. Be Entropy. LEDFlow: Introducing Entropy-guided Generation Order into Uniform Discrete Flow](https://mlsanity.com/paper/2609.25131/) (2026)
- [Faster Block-Diffusion Serving with Distribution-Free Risk Guarantees](https://mlsanity.com/paper/2609.33887/) (2026)
- [HyperZip: Efficient Data Compression through Personalized Diffusion LLMs with Hypernetworks](https://mlsanity.com/paper/2609.36357/) (2026)
- [Counterfactual Probing for Parallel Unmasking with Hidden Forest Structure](https://mlsanity.com/paper/2609.37841/) (2026)
- [Training Parallel Speculative Draft Models by Directly Minimizing Expected Decoding Rounds](https://mlsanity.com/paper/2610.10411/) (2026)
- [The Lattice of Transition Laws](https://mlsanity.com/paper/2610.11216/) (2026)

## Abstract (arXiv)

Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive (AR) models for language modeling, allowing flexible generation order and parallel generation of multiple tokens. However, this flexibility introduces a challenge absent in AR models: the decoding strategy -- which determines the order and number of tokens generated at each iteration -- critically affects sampling efficiency. Among decoding strategies explored in practice, confidence-based methods, which adaptively select which and how many tokens to unmask based on prediction confidence, have shown strong empirical performance. Despite this success, our theoretical understanding of confidence-based decoding remains limited. In this work, we develop the first theoretical analysis framework for confidence-based decoding in DLMs. We focus on an entropy sum-based strategy that continues unmasking tokens within each iteration until the cumulative entropy exceeds a threshold, and show that it achieves varepsilon-accurate sampling in KL divergence with an expected number of iterations widetilde O(H(X0)/varepsilon), where H(X0) denotes the entropy of the target data distribution. Notably, this strategy yields substantial sampling acceleration when the data distribution has low entropy relative to the sequence length, while automatically adapting to the intrinsic complexity of data without requiring prior knowledge or hyperparameter tuning. Overall, our results provide a theoretical foundation for confidence-based decoding and may inform the design of more efficient decoding strategies for DLMs.