mlsanityData to 7 Oct 2026

Language Generation as Optimal Control: Closed-Loop Diffusion in Latent Control Space

arXiv 2605.14531 ↗First posted 14 May 2026cs.CLcited by 0

On the map: Diffusion models → Discrete and text diffusion

Abstract (arXiv)

This work reformulates language generation as a stochastic optimal control problem, providing a unified theoretical perspective to analyze autoregressive and diffusion models and explain their limitations (Efficiency-Fidelity Paradox, Irreversibility Error Propagation, Optimization Tractability and Fidelity) in terms of combination of trajectory singularity, adjoint state vanishing, and gradient absence. To address these issues, we approximate the solution to the Hamilton-Jacobi-Bellman (HJB) equation, yielding an optimal policy that acts as a closed-loop controller. To bypass the intractability of directly solving the HJB PDE, we employ Flow Matching as the optimal trajectory solver within the rectified latent control space. This allows our Manta-LM with Global Integral Operator to approximate the global vector field, effectively realizing a model that simultaneously achieves high-fidelity text generation and efficient, low-cost parallel sampling. Empirically, our method achieves strong performance on language modeling and conditional generation tasks, while exhibiting improved stability, efficiency, and controllability.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Discrete and text diffusion, one of 14 directions in Diffusion models. Builds on 37 of its 48 references that are in the map. First posted on arXiv 14 May 2026.

Builds on

37 of 48 references.

Closest ancestors · 15

Same direction, newest first

  1. 2025Dream 7B: Diffusion Large Language Models21 Aug
  2. 2025Continuous Diffusion Model for Language Modeling17 Feb
  3. 2025Large Language Diffusion Models14 Feb
  4. 2024Scaling Diffusion Language Models via Adaptation from Autoregressive Models23 Oct
  5. 2024Simple and Effective Masked Diffusion Language Models11 Jun
  6. 2024Simplified and Generalized Masked Diffusion for Discrete Data6 Jun
  7. 2024Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data6 Jun
  8. 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution25 Oct
  9. 2023DiffuSeq-v2: Bridging Discrete and Continuous Text Spaces for Accelerated Seq2Seq Diffusion Models9 Oct
  10. 2023Likelihood-Based Diffusion Language Models30 May
  11. 2023TESS: Text-to-Text Self-Conditioned Simplex Diffusion15 May
  12. 2022Continuous diffusion for categorical data28 Nov
3 more
  1. 2022Self-conditioned Embedding Diffusion for Text Generation8 Nov
  2. 2022SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control31 Oct
  3. 2022DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models17 Oct

Other references · 22

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2023LLaMA: Open and Efficient Foundation Language Modelscited by 13,958
  3. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2022Flow Matching for Generative Modelingcited by 5,426
  6. 2016Pointer Sentinel Mixture Modelscited by 2,992
  7. 2024Qwen2 Technical Reportcited by 2,076
  8. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  9. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
  10. 2016The LAMBADA dataset: Word prediction requiring a broad discourse contextcited by 960
  11. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  12. 2013One Billion Word Benchmark for Measuring Progress in Statistical Language Modelingcited by 302
10 more
  1. 2025MMaDA: Multimodal Large Diffusion Language Modelscited by 241
  2. 2024Deep Compression Autoencoder for Efficient High-Resolution Diffusion Modelscited by 209
  3. 2022Score-based Continuous-time Discrete Diffusion Modelscited by 167
  4. 2025AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning datasetcited by 165
  5. 2024OpenCoder: The Open Cookbook for Top-Tier Code Large Language Modelscited by 127
  6. 2020Neural CRF Model for Sentence Alignment in Text Simplificationcited by 106
  7. 2017Quasar: Datasets for Question Answering by Search and Readingcited by 50
  8. 2025Infinity Instruct: Scaling Instruction Selection and Synthesis to Enhance Language Modelscited by 49
  9. 2024Categorical Flow Matching on Statistical Manifoldscited by 43
  10. 2023Stochastic optimal transport and Hamilton-Jacobi-Bellman equations on the set of probability measurescited by 1

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