# Planner Aware Path Learning in Diffusion Language Models Training

arXiv: https://arxiv.org/abs/2509.23405 · HTML: https://mlsanity.com/paper/2509.23405/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 39 of its 53 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 39)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [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)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (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)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Scaling Diffusion Language Models via Adaptation from Autoregressive Models](https://mlsanity.com/paper/2410.17891/) (2024)
- [Efficient Training of Language Models to Fill in the Middle](https://mlsanity.com/paper/2207.14255/) (2022)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Sampling](https://mlsanity.com/paper/2409.02908/) (2024)
- [Scaling up Masked Diffusion Models on Text](https://mlsanity.com/paper/2410.18514/) (2024)
- [Remasking Discrete Diffusion Models with Inference-Time Scaling](https://mlsanity.com/paper/2503.00307/) (2025)
- [Seed Diffusion: A Large-Scale Diffusion Language Model with High-Speed Inference](https://mlsanity.com/paper/2508.02193/) (2025)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [ProGen2: Exploring the Boundaries of Protein Language Models](https://mlsanity.com/paper/2206.13517/) (2022)
- [Simple Guidance Mechanisms for Discrete Diffusion Models](https://mlsanity.com/paper/2412.10193/) (2024)
- [A Reparameterized Discrete Diffusion Model for Text Generation](https://mlsanity.com/paper/2302.05737/) (2023)
- [Diffusion Language Models Are Versatile Protein Learners](https://mlsanity.com/paper/2402.18567/) (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)

## Built on by (most cited first, 14 of 14)

- [Stop Training for the Worst: Progressive Unmasking Accelerates Masked Diffusion Training](https://mlsanity.com/paper/2602.10314/) (2026)
- [DUEL: Exact Likelihood for Masked Diffusion via Deterministic Unmasking](https://mlsanity.com/paper/2603.01367/) (2026)
- [Don't Retrain, Align: Adapting Autoregressive LMs to Diffusion LMs via Representation Alignment](https://mlsanity.com/paper/2605.06885/) (2026)
- [Expert-Choice Routing Enables Adaptive Computation in Diffusion Language Models](https://mlsanity.com/paper/2604.01622/) (2026)
- [Coupling Models for One-Step Discrete Generation](https://mlsanity.com/paper/2605.07193/) (2026)
- [A2D2: Fine-Tuning Any-Length Discrete Diffusion for Adaptive Decoding](https://mlsanity.com/paper/2606.13565/) (2026)
- [Distilled Continuous Diffusion Language Models Can Write Code in Few Steps---or One](https://mlsanity.com/paper/2609.04531/) (2026)
- [Learned Relay Representations for Forward-Thinking Discrete Diffusion Models](https://mlsanity.com/paper/2605.22967/) (2026)
- [Looped Diffusion Language Models](https://mlsanity.com/paper/2605.26106/) (2026)
- [The Confidence Shortcut: A Reasoning Failure Mode of Masked Diffusion Models](https://mlsanity.com/paper/2605.29123/) (2026)
- [MemDLM: Memory-Enhanced DLM Training](https://mlsanity.com/paper/2603.22241/) (2026)
- [Understanding and Accelerating the Training of Masked Diffusion Language Models](https://mlsanity.com/paper/2605.13026/) (2026)
- [Adaptive Order Policies for Masked Diffusion](https://mlsanity.com/paper/2606.00295/) (2026)
- [BlockGen: Flexible Blockwise Sequence Modeling with Hybrid Samplers](https://mlsanity.com/paper/2606.02241/) (2026)

## Abstract (arXiv)

Diffusion language models have emerged as a powerful alternative to autoregressive models, enabling fast inference through more flexible and parallel generation paths. This flexibility of sampling is unlocked by new engineered sampling strategies, or planners, that select more favorable generation paths by iteratively planning - versus uniformly at random - where to denoise along the sequence. However, by modifying the reverse paths via planning, planners create an irrevocable mismatch between the uniformly random denoising paths assumed during training and planning-based inference. In this paper, we systematically investigate the mismatch of discrete diffusion training and inference under planning and theoretically prove that the standard discrete diffusion training evidence lower bound (ELBO) does not accurately describe a denoiser that uses a non-uniform planner. To address this gap, we derive a new planned evidence lower bound (P-ELBO) that incorporates planner-based reverse dynamics directly into the training objective. Using the P-ELBO, we introduce Planner Aware Path Learning (PAPL), a novel training scheme that aligns training and inference under a planned denoiser. PAPL is implemented as a simple yet effective modification to the standard masked discrete diffusion loss, making it widely applicable and easy to adopt. Empirically, we show PAPL delivers consistent gains across domains, including a 40% relative improvement in protein sequences, improved text generation with up to a 4x relative MAUVE gain, and 23% relative improvement in code generation HumanEval pass@10. Code is available at github.com/pengzhangzhi/PAPL .