# Consistent Diffusion Language Models

arXiv: https://arxiv.org/abs/2605.00161 · HTML: https://mlsanity.com/paper/2605.00161/

## 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 8 of its 35 references that are in the map.
- First posted on arXiv 30 Apr 2026.

## Placed in

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

## Builds on (most cited first, 8 of 8)

- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [dLLM-Cache: Accelerating Diffusion Large Language Models with Adaptive Caching](https://mlsanity.com/paper/2506.06295/) (2025)
- [Simple Guidance Mechanisms for Discrete Diffusion Models](https://mlsanity.com/paper/2412.10193/) (2024)
- [Accelerated Sampling from Masked Diffusion Models via Entropy Bounded Unmasking](https://mlsanity.com/paper/2505.24857/) (2025)
- [Multistep Consistency Models](https://mlsanity.com/paper/2403.06807/) (2024)
- [DPad: Efficient Diffusion Language Models with Suffix Dropout](https://mlsanity.com/paper/2508.14148/) (2025)
- [Empirical Analysis of Decoding Biases in Masked Diffusion Models](https://mlsanity.com/paper/2508.13021/) (2025)
- [Reward-Weighted Sampling: Enhancing Non-Autoregressive Characteristics in Masked Diffusion LLMs](https://mlsanity.com/paper/2509.00707/) (2025)

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

- [Continuous Language Diffusion as a Decoder-Interface Problem](https://mlsanity.com/paper/2606.08810/) (2026)
- [Simple Diffusion Language Models Are More Effective Few-Step Generators Than Reported](https://mlsanity.com/paper/2609.33947/) (2026)

## Abstract (arXiv)

Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps. In continuous domains, consistency training along the probability-flow ODE is a popular recipe to accelerate diffusion. For discrete diffusion, no analogous sample-space ODE exists, making direct adaptation ill-defined. We argue that the right discrete substitute is the exact posterior bridge, the closed-form conditional law linking any two noise levels, which is available for broad corruptions including masked and uniform diffusion. Building on this observation, we introduce Multi-Path Discrete Consistency (MPDC), a new principle that trains a denoiser to be path-invariant in expectation across these stochastic bridges, and instantiate it as the Consistent Diffusion Language Model (CDLM), a single-stage training framework that does not require an already trained teacher model. Our CDLM objective recovers masked diffusion, continuous consistency models, and progressive or discrete distillation as analytic limits or empirical approximations of one common view. Empirically, CDLM establishes a new state of the art on both conditional and unconditional text-generation, consistently outperforming strong base discrete diffusion models and often even multi-stage distilled baselines across sampling budgets, with the largest gains in the few-step regime. Together, these results position CDLM as a principled and scalable foundation for the next generation of fast, high-fidelity discrete generative modeling.