# Discrete Diffusion Models Exploit Asymmetry to Solve Lookahead Planning Tasks

arXiv: https://arxiv.org/abs/2602.19980 · HTML: https://mlsanity.com/paper/2602.19980/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 30 of its 33 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Placed in

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

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [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)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [On the Planning Abilities of Large Language Models : A Critical Investigation](https://mlsanity.com/paper/2305.15771/) (2023)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Large Language Models Empowered Agent-based Modeling and Simulation: A Survey and Perspectives](https://mlsanity.com/paper/2312.11970/) (2023)
- [Can Language Models Solve Graph Problems in Natural Language?](https://mlsanity.com/paper/2305.10037/) (2023)
- [Language is All a Graph Needs](https://mlsanity.com/paper/2308.07134/) (2023)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Plan-and-Act: Improving Planning of Agents for Long-Horizon Tasks](https://mlsanity.com/paper/2503.09572/) (2025)
- [Large Language Models on Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2312.02783/) (2023)
- [Talk like a Graph: Encoding Graphs for Large Language Models](https://mlsanity.com/paper/2310.04560/) (2023)
- [Birth of a Transformer: A Memory Viewpoint](https://mlsanity.com/paper/2306.00802/) (2023)
- [The pitfalls of next-token prediction](https://mlsanity.com/paper/2403.06963/) (2024)
- [Beyond Autoregression: Discrete Diffusion for Complex Reasoning and Planning](https://mlsanity.com/paper/2410.14157/) (2024)
- [Accelerated Sampling from Masked Diffusion Models via Entropy Bounded Unmasking](https://mlsanity.com/paper/2505.24857/) (2025)
- [Unveiling Transformers with LEGO: a synthetic reasoning task](https://mlsanity.com/paper/2206.04301/) (2022)
- [Understanding Transformer Reasoning Capabilities via Graph Algorithms](https://mlsanity.com/paper/2405.18512/) (2024)
- [Overparameterized Neural Networks Implement Associative Memory](https://mlsanity.com/paper/1909.12362/) (2019)
- [Set Block Decoding is a Language Model Inference Accelerator](https://mlsanity.com/paper/2509.04185/) (2025)
- [Transformers Struggle to Learn to Search](https://mlsanity.com/paper/2412.04703/) (2024)
- [Deep sequence models tend to memorize geometrically; it is unclear why](https://mlsanity.com/paper/2510.26745/) (2025)
- [The Mystery of the Pathological Path-star Task for Language Models](https://mlsanity.com/paper/2410.13779/) (2024)

## Built on by (most cited first, 4 of 4)

- [Locally Confident, Globally Stuck: The Quality-Exploration Dilemma in Diffusion Language Models](https://mlsanity.com/paper/2604.00375/) (2026)
- [From Interface to Inference: Eliciting Any-Order Inference from Any-Order Models](https://mlsanity.com/paper/2607.26504/) (2026)
- [Retrofitting Linear Attention into Diffusion Language Models](https://mlsanity.com/paper/2608.06628/) (2026)
- [Plan-and-Patch: Diffusion Language Models for Agentic Planning](https://mlsanity.com/paper/2610.10786/) (2026)

## Abstract (arXiv)

While Autoregressive (AR) Transformer-based Generative Language Models are frequently employed for lookahead tasks, recent research suggests a potential discrepancy in their ability to perform planning tasks that require multi-step lookahead. In this work, we investigate the distinct emergent mechanisms that arise when training AR versus Non-Autoregressive (NAR) models, such as Discrete Diffusion Models (dLLMs), on lookahead tasks. By requiring the models to plan ahead to reach the correct conclusion, we analyze how these two paradigms fundamentally differ in their approach to the problem. We identify a critical asymmetry in planning problems: while forward generation requires complex lookahead at branching junctions, reverse generation is often deterministic. This asymmetry creates an opportunity for NAR models. Through mechanistic analysis of training and inference dynamics, we demonstrate that NAR models learn to solve planning tasks by utilizing future tokens to decode backwards, avoiding the need to learn complex traversal mechanisms entirely. Consequently, we report that both AR and NAR models are able to achieve perfect accuracy on the lookahead task. However, NAR models require exponentially fewer training examples and shallower architectures compared to AR models, which often fail to converge without specific curriculum adjustments.