# ELF-REG: Scaling Continuous Diffusion Language Models to Reasoning Tasks

arXiv: https://arxiv.org/abs/2609.29102 · HTML: https://mlsanity.com/paper/2609.29102/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion reasoning and test-time scaling, one of 17 directions in LLM reasoning.
- Builds on 42 of its 44 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Placed in

- LLM reasoning / [Diffusion reasoning and test-time scaling](https://mlsanity.com/lr/diffusion-reasoning-and-test-time-scaling/)
- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 30 of 42)

- [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)
- [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)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [The Diffusion Duality](https://mlsanity.com/paper/2506.10892/) (2025)
- [Flow map matching with stochastic interpolants: A mathematical framework for consistency models](https://mlsanity.com/paper/2406.07507/) (2024)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Representation Entanglement for Generation: Training Diffusion Transformers Is Much Easier Than You Think](https://mlsanity.com/paper/2507.01467/) (2025)
- [Diffusion Language Models Know the Answer Before Decoding](https://mlsanity.com/paper/2508.19982/) (2025)
- [Flow Map Language Models: One-step Language Modeling via Continuous Denoising](https://mlsanity.com/paper/2602.16813/) (2026)
- [OpenCodeInstruct: A Large-scale Instruction Tuning Dataset for Code LLMs](https://mlsanity.com/paper/2504.04030/) (2025)
- [Falcon-H1: A Family of Hybrid-Head Language Models Redefining Efficiency and Performance](https://mlsanity.com/paper/2507.22448/) (2025)
- [No Other Representation Component Is Needed: Diffusion Transformers Can Provide Representation Guidance by Themselves](https://mlsanity.com/paper/2505.02831/) (2025)
- [Edit Flows: Flow Matching with Edit Operations](https://mlsanity.com/paper/2506.09018/) (2025)
- [Empowering Diffusion Models on the Embedding Space for Text Generation](https://mlsanity.com/paper/2212.09412/) (2022)
- [REPA Works Until It Doesn't: Early-Stopped, Holistic Alignment Supercharges Diffusion Training](https://mlsanity.com/paper/2505.16792/) (2025)
- [Continuously Augmented Discrete Diffusion model for Categorical Generative Modeling](https://mlsanity.com/paper/2510.01329/) (2025)
- [Coevolutionary Continuous Discrete Diffusion: Make Your Diffusion Language Model a Latent Reasoner](https://mlsanity.com/paper/2510.03206/) (2025)

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

- [Reasoning with Continuous Latent Diffusion](https://mlsanity.com/paper/2609.35694/) (2026)

## Abstract (arXiv)

Fully continuous diffusion language models (dLMs) denoise continuous representations without intermediate discretization, then decode all response tokens in parallel at the final step. Their performance on challenging reasoning tasks remains less established than that of autoregressive (AR) LLMs and masked dLMs. We scale Embedded Language Flows (ELF) to mathematical reasoning and code generation on GSM8K, MATH-500, HumanEval, and MBPP. We introduce ELF-REG, which improves learning with representation alignment and entanglement (REPA+REG), where a frozen AR teacher supervises intermediate denoiser features and supplies a global representation that is jointly denoised with the response. ELF-REG-L achieves 55.96% pass@1 on GSM8K at 64 network function evaluations (NFE), and 13.39% on MATH-500 and 22.56% on HumanEval at 128 NFE. It outperforms the evaluated comparable-scale dLMs in pass@1 on GSM8K and code, and improves MATH-500 pass@1 from 10.55% for the ELF-L baseline to 13.39% with ELF-REG-L. Without few-step training, the same task-specific checkpoints support strong low-NFE performance through early-stop, which decodes an intermediate clean prediction without completing the denoising trajectory. At 16 NFE, ELF-REG-L reaches 41.21% HumanEval pass@10, outperforming recent continuous dLMs of comparable scale.