# VDLM: Variable Diffusion LMs via Robust Latent-to-Text Rendering

arXiv: https://arxiv.org/abs/2602.15870 · HTML: https://mlsanity.com/paper/2602.15870/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 31 of its 50 references that are in the map.
- First posted on arXiv 27 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 31)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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 Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [DiffusionBERT: Improving Generative Masked Language Models with Diffusion Models](https://mlsanity.com/paper/2211.15029/) (2022)
- [Text Embeddings Reveal (Almost) As Much As Text](https://mlsanity.com/paper/2310.06816/) (2023)
- [LLaDA2.0: Scaling Up Diffusion Language Models to 100B](https://mlsanity.com/paper/2512.15745/) (2025)
- [Generalization in Generation: A closer look at Exposure Bias](https://mlsanity.com/paper/1910.00292/) (2019)
- [Accelerating Diffusion LLMs via Adaptive Parallel Decoding](https://mlsanity.com/paper/2506.00413/) (2025)
- [Why Exposure Bias Matters: An Imitation Learning Perspective of Error Accumulation in Language Generation](https://mlsanity.com/paper/2204.01171/) (2022)
- [Diffusion Beats Autoregressive in Data-Constrained Settings](https://mlsanity.com/paper/2507.15857/) (2025)
- [Discrete Diffusion in Large Language and Multimodal Models: A Survey](https://mlsanity.com/paper/2506.13759/) (2025)
- [Semi-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/1808.08583/) (2018)
- [Exposure Bias versus Self-Recovery: Are Distortions Really Incremental for Autoregressive Text Generation?](https://mlsanity.com/paper/1905.10617/) (2019)
- [Language Models are Injective and Hence Invertible](https://mlsanity.com/paper/2510.15511/) (2025)
- [AdaBlock-dLLM: Semantic-Aware Diffusion LLM Inference via Adaptive Block Size](https://mlsanity.com/paper/2509.26432/) (2025)
- [d2: Improving Reasoning in Diffusion Language Models via Trajectory Likelihood Estimation](https://mlsanity.com/paper/2509.21474/) (2025)
- [Emergence of Superposition: Unveiling the Training Dynamics of Chain of Continuous Thought](https://mlsanity.com/paper/2509.23365/) (2025)

## Built on by (most cited first, 1 of 1)

- [From Interface to Inference: Eliciting Any-Order Inference from Any-Order Models](https://mlsanity.com/paper/2607.26504/) (2026)

## Abstract (arXiv)

Autoregressive language models decode left-to-right with irreversible commitments, limiting revision during multi-step reasoning. We propose VDLM, a modular variable diffusion language model that separates semantic planning from text rendering. VDLM applies LLaDA-style masked diffusion over semantic variable embeddings to enable iterative refinement in latent space, then post-trains the planner with trajectory-aware optimization using embedding-space rewards and values, avoiding text decoding inside the RL loop. To convert planned embeddings back to text, we use a Vec2Text renderer and introduce embedding perturbations to robustify decoding under planner noise. Across nine benchmarks spanning general reasoning, math, and code, VDLM is competitive in pre-training and yields substantial post-training improvements on long-form generation tasks, outperforming other baselines. These results highlight the effectiveness of embedding-space post-training and robust latent-to-text rendering for diffusion language modeling.