# CD4LM: Consistency Distillation and aDaptive Decoding for Diffusion Language Models

arXiv: https://arxiv.org/abs/2601.02236 · HTML: https://mlsanity.com/paper/2601.02236/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 34 of its 39 references that are in the map.
- First posted on arXiv 5 Jan 2026.

## Placed in

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

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (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)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [Mercury: Ultra-Fast Language Models Based on Diffusion](https://mlsanity.com/paper/2506.17298/) (2025)
- [DiffuCoder: Understanding and Improving Masked Diffusion Models for Code Generation](https://mlsanity.com/paper/2506.20639/) (2025)
- [dLLM-Cache: Accelerating Diffusion Large Language Models with Adaptive Caching](https://mlsanity.com/paper/2506.06295/) (2025)
- [Likelihood-Based Diffusion Language Models](https://mlsanity.com/paper/2305.18619/) (2023)
- [Beyond Autoregression: Discrete Diffusion for Complex Reasoning and Planning](https://mlsanity.com/paper/2410.14157/) (2024)
- [Accelerating Diffusion LLMs via Adaptive Parallel Decoding](https://mlsanity.com/paper/2506.00413/) (2025)
- [Dimple: Discrete Diffusion Multimodal Large Language Model with Parallel Decoding](https://mlsanity.com/paper/2505.16990/) (2025)
- [OpenCodeInstruct: A Large-scale Instruction Tuning Dataset for Code LLMs](https://mlsanity.com/paper/2504.04030/) (2025)
- [Speculative Diffusion Decoding: Accelerating Language Generation through Diffusion](https://mlsanity.com/paper/2408.05636/) (2024)
- [Reinforcing the Diffusion Chain of Lateral Thought with Diffusion Language Models](https://mlsanity.com/paper/2505.10446/) (2025)

## Built on by (most cited first, 8 of 8)

- [JetSpec: Breaking the Scaling Ceiling of Speculative Decoding with Parallel Tree Drafting](https://mlsanity.com/paper/2606.18394/) (2026)
- [Learning from the Self-future: On-policy Self-distillation for dLLMs](https://mlsanity.com/paper/2606.18195/) (2026)
- [ECHO: Efficient Chest X-ray Report Generation with One-step Block Diffusion](https://mlsanity.com/paper/2604.09450/) (2026)
- [TAD: Temporal-Aware Trajectory Self-Distillation for Fast and Accurate Diffusion LLM](https://mlsanity.com/paper/2605.09536/) (2026)
- [Distilled Continuous Diffusion Language Models Can Write Code in Few Steps---or One](https://mlsanity.com/paper/2609.04531/) (2026)
- [Not All Denoising Steps Are Equal: Model Scheduling for Faster Masked Diffusion Language Models](https://mlsanity.com/paper/2604.02340/) (2026)
- [Latent Shadows: The Gaussian-Discrete Duality in Masked Diffusion](https://mlsanity.com/paper/2602.00792/) (2026)
- [Early-Bird Decoding: Accelerating Diffusion LLMs with Learnable Block Sizes and Parallel Sampling](https://mlsanity.com/paper/2609.16450/) (2026)

## Abstract (arXiv)

Autoregressive large language models achieve strong results on many benchmarks, but decoding remains fundamentally latency-limited by sequential dependence on previously generated tokens. Diffusion language models (DLMs) promise parallel generation but suffer from a fundamental static-to-dynamic misalignment: Training optimizes local transitions under fixed schedules, whereas efficient inference requires adaptive "long-jump" refinements through unseen states. Our goal is to enable highly parallel decoding for DLMs with low number of function evaluations while preserving generation quality. To achieve this, we propose CD4LM, a framework that decouples training from inference via Discrete-Space Consistency Distillation (DSCD) and Confidence-Adaptive Decoding (CAD). Unlike standard objectives, DSCD trains a student to be trajectory-invariant, mapping diverse noisy states directly to the clean distribution. This intrinsic robustness enables CAD to dynamically allocate compute resources based on token confidence, aggressively skipping steps without the quality collapse typical of heuristic acceleration. On GSM8K, CD4LM matches the LLaDA baseline with a 5.18x wall-clock speedup; across code and math benchmarks, it strictly dominates the accuracy-efficiency Pareto frontier, achieving a 3.62x mean speedup while improving average accuracy. Code is available at https://github.com/yihao-liang/CDLM