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arxiv: 2605.14531 · v3 · pith:SQFVJQUWnew · submitted 2026-05-14 · 💻 cs.CL

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

ZiYi Dong , Yuliang Huang , Weijian Deng , Xiangyang Ji , Liang Lin , Pengxu Wei This is my paper

Pith reviewed 2026-06-30 21:13 UTC · model grok-4.3

classification 💻 cs.CL
keywords language generationoptimal controlHamilton-Jacobi-Bellman equationflow matchingdiffusion modelslatent control spaceautoregressive modelsparallel sampling
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The pith

Language generation is reframed as a stochastic optimal control problem whose solution yields both high-fidelity output and efficient parallel sampling.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper casts language generation as a stochastic optimal control task to give a single theoretical account of autoregressive and diffusion models. It traces their shared shortcomings to trajectory singularity, adjoint state vanishing, and missing gradients. Approximating the Hamilton-Jacobi-Bellman equation inside a rectified latent control space supplies an optimal closed-loop policy. Flow Matching serves as the trajectory solver and the Global Integral Operator inside Manta-LM approximates the global vector field, producing a model that keeps high fidelity while allowing cheap parallel sampling.

Core claim

By treating language generation as stochastic optimal control, the solution to the Hamilton-Jacobi-Bellman equation is approximated with Flow Matching acting as the optimal trajectory solver in the rectified latent control space. The resulting Manta-LM equipped with the Global Integral Operator approximates the global vector field and thereby implements the optimal closed-loop controller, delivering high-fidelity text generation together with efficient low-cost parallel sampling.

What carries the argument

Flow Matching as the optimal trajectory solver inside the rectified latent control space, realized through the Global Integral Operator in Manta-LM that approximates the global vector field.

If this is right

  • The Efficiency-Fidelity Paradox, Irreversibility Error Propagation, Optimization Tractability, and Fidelity limitations are simultaneously addressed.
  • A single model achieves both the fidelity of autoregressive generation and the parallel sampling speed of diffusion models.
  • Improved stability, efficiency, and controllability are observed on language modeling and conditional generation tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same control-space construction could be tested on other sequence tasks such as code or protein generation.
  • Because the policy is closed-loop, it may reduce error accumulation over very long outputs compared with open-loop diffusion.
  • Replacing Flow Matching with other trajectory solvers inside the same latent control space offers a direct route to further efficiency gains.

Load-bearing premise

Flow Matching inside the rectified latent control space can accurately approximate the global vector field and thereby implement the optimal closed-loop policy obtained from the Hamilton-Jacobi-Bellman equation.

What would settle it

An experiment in which Manta-LM is run on standard language-modeling and conditional-generation benchmarks and produces measurably lower fidelity than strong diffusion baselines at comparable sampling cost would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.14531 by Liang Lin, Pengxu Wei, Weijian Deng, Xiangyang Ji, Yuliang Huang, ZiYi Dong.

Figure 1
Figure 1. Figure 1: Generation dynamics. On a non-convex manifold, (a) AR and Diffusion are trapped in a slow, myopic crawl along the high-curvature density ridge. (b) In contrast, our method approx￾imates the global optimal trajectory, bypassing curvature via the rectified latent geometry (energy-minimizing geodesic) for im￾proved efficiency. the optimal controller in Equation (3), targeting high data fidelity with low infer… view at source ↗
Figure 1
Figure 1. Figure 1: Generation dynamics. On a non-convex manifold, (a) AR and Diffusion are trapped in a slow, myopic crawl along the high-curvature density ridge. (b) In contrast, our method approx￾imates the global optimal trajectory, bypassing curvature via the rectified latent geometry (energy-minimizing geodesic) for im￾proved efficiency. ii) Lyapunov Instability: Without the restoring force pro￾vided by the adjoint feed… view at source ↗
Figure 2
Figure 2. Figure 2: Visualizing Generative Dynamics and Error Propa￾gation on BVP task. Color from pink to blue denotes generation progress. (a) AR suffers from compounding errors (blue lines in (d)) due to open-loop myopia, drifting off-manifold. (b) Discrete DLM relies on stochastic combinatorial search showing jagged tra￾jectories caused by geometric blindness (lack of gradients). (c) Our Manta-LM acts as an optimal closed… view at source ↗
Figure 3
Figure 3. Figure 3: Geometric comparison. Unlike (a) Autoregressive models’ serial paths or (b-c) Diffusion baselines’ high-curvature trajectories in ill-conditioned spaces, (d) Ours operates on a recti￾fied latent manifold. The learned optimal vector field vθ enables energy-minimizing, straight-line transport from noise to data. 4.1. Control-Friendly Manifold Rectification Rectification via Diffeomorphism. We introduce a Var… view at source ↗
Figure 3
Figure 3. Figure 3: Geometric comparison. Unlike (a) Autoregressive models’ serial paths or (b-c) Diffusion baselines’ high-curvature trajectories in ill-conditioned spaces, (d) Ours operates on a recti￾fied latent manifold. The learned optimal vector field vθ enables energy-minimizing, straight-line transport from noise to data [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Efficiency evaluation with inference throughput. transforming the ill-conditioned high-frequency regression problem into a well-conditioned one, thereby making the HJB-inspired dynamics easier to approximate with Flow Matching and efficient large-step integration. Geometric Regularity and Optimization Stability. Fig￾ure 6 contrasts the rugged optimization landscape of discrete baselines, which reflects sev… view at source ↗
Figure 5
Figure 5. Figure 5: Stiffness Analysis. The raw Token (Embedding) Space exhibits extreme stiffness and high curvature, indicating an ill￾conditioned control landscape that forces adaptive solvers (RK45) to high NFE. In contrast, our Rectified Latent Space maintains low stiffness and near-linear trajectories, verifying the efficacy of VAE. (a) Auto-Regressive (GPT-2) (b) Discrete Diffusion (RADD) (c) Manta-LM (Ours) [PITH_FUL… view at source ↗
Figure 6
Figure 6. Figure 6: Optimization landscapes of different generation paradigms. (a) AR exhibits sharp and unstable geometry. (b) Discrete diffusion leads to fragmented and irregular landscapes. (c) Our Manta-LM yields a smooth and well-conditioned land￾scape, enabling stable optimization. 6. Conclusion We presented Manta-LM, a framework that studies and re￾imagines text generation as Stochastic Optimal Control prob￾lem. By app… view at source ↗
Figure 7
Figure 7. Figure 7: Model structure and pipeline. due to the high-frequency discontinuities of the semantic energy landscape V across discrete tokens, no single vector v can satisfy the first-order Taylor approximation for the local neighborhood, formally implying that ∄ v such that V (z + d) − V (z) ≈ ⟨v, d⟩ holds, thereby confirming the structural absence of gradient guidance. ∄ v ∈ TzM s.t. ⟨v, d⟩ ≈ V (z + d) − V (z). (24)… view at source ↗
Figure 8
Figure 8. Figure 8: Analysis on interplay between CFG guidance strength and integration fidelity • Optimal Regime (w ∈ [3.0, 5.0]): This setting achieves the best quality-efficiency trade-off. Metrics saturate rapidly (within 20–30 steps), indicating that the vector field is sufficiently aligned with the condition while remaining smooth enough for coarse-step integration. • Over-Guided Regime (w ≥ 7.0): We observe a sharp per… view at source ↗
Figure 9
Figure 9. Figure 9: Step-by-step conditional generation process of Manta-LM on a paraphrase task. Given the input sentence “what was the best day of your life, and what happened?”, the figure visualizes the intermediate generation trajectories of Manta-LM across diffusion steps. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Step-by-step conditional generation process of Manta-LM on a paraphrase task. Given the input sentence “how can i be a good geologist?”, the figure visualizes the intermediate generation trajectories of Manta-LM across diffusion steps. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Visualizing error correction capabilities across different models. Red text indicates corrupted or erroneous tokens introduced by noise. while yellow text denotes tokens that are semantically consistent with the ground-truth text but differ in surface form. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Qualitative examples of the text infilling task. Text in blue represents the provided prefix and suffix, while text in black denotes the model’s generated results. Rabat – Dutch far-right lawmaker Geert Wilders was found not guilty of hate speech but guilty of discrimination and group insult. He will face no punishment. The verdict is in reference to comments Wilders, the leader of the Freedom Party, made… view at source ↗
Figure 13
Figure 13. Figure 13: Qualitative examples of the text infilling task. Text in blue represents the provided prefix and suffix, while text in black denotes the model’s generated results. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Qualitative examples of the text infilling task. Text in blue represents the provided prefix and suffix, while text in black denotes the model’s generated results. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper reformulates language generation as a stochastic optimal control problem to unify autoregressive and diffusion models and explain their limitations (Efficiency-Fidelity Paradox, Irreversibility Error Propagation, Optimization Tractability and Fidelity) via trajectory singularity, adjoint state vanishing, and gradient absence. It approximates the Hamilton-Jacobi-Bellman (HJB) equation solution to obtain an optimal closed-loop policy, using Flow Matching as the trajectory solver inside a rectified latent control space together with a Global Integral Operator to yield the Manta-LM model, which is claimed to deliver high-fidelity generation with efficient parallel sampling. Strong empirical performance is asserted on language modeling and conditional generation tasks.

Significance. If the central identification between the Flow Matching velocity field and the HJB-derived optimal policy holds, the work would supply a principled control-theoretic account of existing generative paradigms and a practical route to controllable, high-fidelity parallel sampling. The explicit treatment of irreversibility and adjoint vanishing as sources of error is a potentially useful diagnostic lens.

major comments (2)
  1. [Abstract] Abstract: The claim that Flow Matching within the rectified latent control space approximates the HJB solution and thereby realizes the optimal closed-loop policy is presented without any derivation showing that the learned velocity field satisfies the nonlinear first-order HJB PDE or yields an (ε-)optimal policy for the underlying stochastic control problem on discrete token sequences. Flow Matching minimizes a regression objective on a prescribed path while HJB optimality is a PDE condition on the value function; the required equivalence is load-bearing for every subsequent claim about optimality, efficiency, and the Efficiency-Fidelity Paradox.
  2. [Abstract] Abstract: The 'rectified latent control space' and 'Global Integral Operator' are introduced as the mechanisms that make the HJB approximation tractable, yet no definition, construction, or proof is supplied that these objects produce a vector field whose integral curves coincide with the optimal policy. This identification is the sole justification for bypassing direct HJB solution and for asserting simultaneous high fidelity and low-cost parallel sampling.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for identifying the need for clearer theoretical grounding in the abstract. We address each point below and commit to revisions that strengthen the presentation without altering the core claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that Flow Matching within the rectified latent control space approximates the HJB solution and thereby realizes the optimal closed-loop policy is presented without any derivation showing that the learned velocity field satisfies the nonlinear first-order HJB PDE or yields an (ε-)optimal policy for the underlying stochastic control problem on discrete token sequences. Flow Matching minimizes a regression objective on a prescribed path while HJB optimality is a PDE condition on the value function; the required equivalence is load-bearing for every subsequent claim about optimality, efficiency, and the Efficiency-Fidelity Paradox.

    Authors: We agree that the abstract states the central identification concisely. The main text (Sections 3 and 4) derives the link by showing that, once the latent control space is rectified, the Flow Matching regression objective is equivalent to minimizing the HJB residual; the Global Integral Operator supplies the missing adjoint information that prevents vanishing and yields an ε-optimal policy for the discrete-token control problem. To make this explicit at the abstract level we will add a short parenthetical reference to the key proposition in Section 4. revision: yes

  2. Referee: [Abstract] Abstract: The 'rectified latent control space' and 'Global Integral Operator' are introduced as the mechanisms that make the HJB approximation tractable, yet no definition, construction, or proof is supplied that these objects produce a vector field whose integral curves coincide with the optimal policy. This identification is the sole justification for bypassing direct HJB solution and for asserting simultaneous high fidelity and low-cost parallel sampling.

    Authors: Definitions, construction, and the proof that the resulting vector field coincides with the optimal policy appear in Sections 3.2–3.3. The rectified space is obtained by a learned coordinate change that removes trajectory singularities; the Global Integral Operator is the integral form of the value function that recovers the HJB solution from the flow-matching velocity field. We will revise the abstract to include one-sentence characterizations of both objects together with a pointer to the relevant sections. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The abstract and provided text reformulate language generation as a stochastic optimal control problem and posit Flow Matching in rectified latent control space as an approximation to the HJB solution without supplying equations that reduce the central claim to its own inputs by construction. No self-citations, fitted parameters renamed as predictions, or self-definitional steps are exhibited. The identification of Flow Matching with the optimal policy is presented as a methodological choice to bypass intractability, supported by empirical results on language tasks, rendering the chain independent of the target result itself.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The approach rests on the validity of modeling generation as stochastic optimal control and the effectiveness of flow matching in the proposed latent space; no free parameters or invented entities are explicitly quantified in the abstract.

axioms (1)
  • domain assumption Language generation can be reformulated as a stochastic optimal control problem whose solution is given by the HJB equation.
    Stated directly in the abstract as the starting point for the unified perspective.
invented entities (1)
  • Rectified latent control space no independent evidence
    purpose: Space in which flow matching approximates the global vector field to realize the optimal policy.
    Introduced to bypass direct intractability of the HJB PDE.

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Works this paper leans on

48 extracted references · 19 canonical work pages · 11 internal anchors

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

  2. [2]

    D., Ho, J., Tarlow, M., and van den Berg, R

    Austin, J., Johnson, D. D., Ho, J., Tarlow, M., and van den Berg, R. Structured denoising diffusion models in discrete state-spaces. In Advances in Neural Information Processing Systems, volume 34, pp.\ 17981--17993, 2021

    2021

  3. [3]

    and Brenier, Y

    Benamou, J.-D. and Brenier, Y. A computational fluid mechanics solution to the monge-kantorovich mass transfer problem. Numerische Mathematik, 84 0 (3): 0 375--393, 2000

    2000

  4. [4]

    Stochastic optimal transport and hamilton–jacobi–bellman equations on the set of probability measures

    Bertucci, C. Stochastic optimal transport and hamilton–jacobi–bellman equations on the set of probability measures. Annales de l'Institut Henri Poincar \'e C, Analyse non lin \'e aire , 2023. URL https://api.semanticscholar.org/CorpusID:259095954

    2023

  5. [5]

    D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., et al

    Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., et al. Language models are few-shot learners. In Advances in neural information processing systems, volume 33, pp.\ 1877--1901, 2020

    1901

  6. [6]

    and Lewis, A

    Bullo, F. and Lewis, A. D. Geometric control of mechanical systems. 2004. URL https://api.semanticscholar.org/CorpusID:679624

    2004

  7. [7]

    T., and Robinson, T

    Chelba, C., Mikolov, T., Schuster, M., Ge, Q., Brants, T., Koehn, P. T., and Robinson, T. One billion word benchmark for measuring progress in statistical language modeling. In Interspeech, 2013

    2013

  8. [8]

    arXiv preprint arXiv:2410.10733 (2024) 10

    Chen, J., Cai, H., Chen, J., Xie, E., Yang, S., Tang, H., Li, M., Lu, Y., and Han, S. Deep compression autoencoder for efficient high-resolution diffusion models. arXiv preprint arXiv:2410.10733, 2024

    work page arXiv 2024

  9. [9]

    Categorical flow matching on statistical manifolds

    Cheng, C., Li, J., Peng, J., and Liu, G. Categorical flow matching on statistical manifolds. Advances in Neural Information Processing Systems, 37: 0 54787--54819, 2024

    2024

  10. [10]

    Training Verifiers to Solve Math Word Problems

    Cobbe, K., Kosaraju, V., Bavarian, M., Chen, M., Jun, H., Kaiser, L., Plappert, M., Tworek, J., Hilton, J., Nakano, R., Hesse, C., and Schulman, J. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168, 2021

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  11. [11]

    Quora question pairs

    DataCanary, hilfialkaff, Jiang, L., Risdal, M., Dandekar, N., and tomtung. Quora question pairs. Kaggle Competition, 2017. https://kaggle.com/competitions/quora-question-pairs

    2017

  12. [12]

    Dhingra, B., Mazaitis, K., and Cohen, W. W. Quasar: Datasets for question answering by search and reading. arXiv preprint arXiv:1707.03904, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  13. [13]

    Continuous diffusion for categorical data

    Dieleman, S., Sartran, L., Roshannai, A., Savinov, N., Ganin, Y., Richemond, P. H., Doucet, A., Strudel, R., Dyer, C., Durkan, C., et al. Continuous diffusion for categorical data. arXiv preprint arXiv:2211.15089, 2022

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  14. [14]

    Fleming, W. H. and Rishel, R. W. Deterministic and stochastic optimal control. Springer Science & Business Media, 2012

    2012

  15. [15]

    and Cohen, V

    Gokaslan, A. and Cohen, V. Openwebtext corpus. http://Skylion007.github.io/OpenWebTextCorpus, 2019

    2019

  16. [16]

    Diffuseq-v2: Bridging discrete and continuous text spaces for accelerated seq2seq diffusion models

    Gong, S., Li, M., Feng, J., Wu, Z., and Kong, L. Diffuseq-v2: Bridging discrete and continuous text spaces for accelerated seq2seq diffusion models. In The 2023 Conference on Empirical Methods in Natural Language Processing

    2023

  17. [17]

    Diffuseq: Sequence to sequence text generation with diffusion models

    Gong, S., Li, M., Feng, J., Wu, Z., and Kong, L. Diffuseq: Sequence to sequence text generation with diffusion models. In International Conference on Learning Representations (ICLR 2023)(01/05/2023-05/05/2023, Kigali, Rwanda), 2023

    2023

  18. [18]

    Scaling Diffusion Language Models via Adaptation from Autoregressive Models

    Gong, S., Agarwal, S., Zhang, Y., Ye, J., Zheng, L., Li, M., An, C., Zhao, P., Bi, W., Han, J., et al. Scaling diffusion language models via adaptation from autoregressive models. arXiv preprint arXiv:2410.17891, 2024

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  19. [19]

    and Hashimoto, T

    Gulrajani, I. and Hashimoto, T. B. Likelihood-based diffusion language models. Advances in Neural Information Processing Systems, 36: 0 16693--16715, 2023

    2023

  20. [20]

    Ssd-lm: Semi-autoregressive simplex-based diffusion language model for text generation and modular control

    Han, X., Kumar, S., and Tsvetkov, Y. Ssd-lm: Semi-autoregressive simplex-based diffusion language model for text generation and modular control. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp.\ 11575--11596, 2023

    2023

  21. [21]

    Argmax flows and multinomial diffusion: Learning categorical distributions

    Hoogeboom, E., Nielsen, D., Jaini, P., Forr \'e , P., and Welling, M. Argmax flows and multinomial diffusion: Learning categorical distributions. Advances in neural information processing systems, 34: 0 12454--12465, 2021

    2021

  22. [22]

    K., Xu, W., Hao, J., Song, L., Xu, Y., Yang, J., Liu, J., Zhang, C., et al

    Huang, S., Cheng, T., Liu, J. K., Xu, W., Hao, J., Song, L., Xu, Y., Yang, J., Liu, J., Zhang, C., et al. Opencoder: The open cookbook for top-tier code large language models. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp.\ 33167--33193, 2025

    2025

  23. [23]

    Neural crf model for sentence alignment in text simplification

    Jiang, C., Maddela, M., Lan, W., Zhong, Y., and Xu, W. Neural crf model for sentence alignment in text simplification. arXiv preprint arXiv:2005.02324, 2020

    work page arXiv 2005

  24. [24]

    and Hwang, S

    Jo, J. and Hwang, S. J. Continuous diffusion model for language modeling. In Neural Information Processing Systems, 2025

    2025

  25. [25]

    Infinity instruct: Scaling instruction selection and synthesis to enhance language models,

    Li, J., Du, L., Zhao, H., Zhang, B.-w., Wang, L., Gao, B., Liu, G., and Lin, Y. Infinity instruct: Scaling instruction selection and synthesis to enhance language models. arXiv preprint arXiv:2506.11116, 2025 a

    work page arXiv 2025

  26. [26]

    Lavida-o: Elastic large masked diffusion models for unified multimodal understanding and generation

    Li, S., Gu, J., Liu, K., Lin, Z., Wei, Z., Grover, A., and Kuen, J. Lavida-o: Elastic large masked diffusion models for unified multimodal understanding and generation. arXiv preprint arXiv:2509.19244, 2025 b

    work page arXiv 2025

  27. [27]

    S., and Hashimoto, T

    Li, X., Thickstun, J., Gulrajani, I., Liang, P. S., and Hashimoto, T. B. Diffusion-lm improves controllable text generation. Advances in neural information processing systems, 35: 0 4328--4343, 2022

    2022

  28. [28]

    T., Ben-Hamu, H., Nickel, M., and Le, M

    Lipman, Y., Chen, R. T., Ben-Hamu, H., Nickel, M., and Le, M. Flow matching for generative modeling. In International Conference on Learning Representations, 2023

    2023

  29. [29]

    Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution

    Lou, A., Meng, C., and Ermon, S. Discrete diffusion modeling by estimating the ratios of the data distribution. arXiv preprint arXiv:2310.16834, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  30. [30]

    K., Ivison, H., Tae, J., Henderson, J., Beltagy, I., Peters, M

    Mahabadi, R. K., Ivison, H., Tae, J., Henderson, J., Beltagy, I., Peters, M. E., and Cohan, A. Tess: Text-to-text self-conditioned simplex diffusion. In Proceedings of the 18th Conference of the European Chapter of the Association for Computational Linguistics (Volume 1: Long Papers), pp.\ 2347--2361, 2024

    2024

  31. [31]

    Pointer sentinel mixture models, 2016

    Merity, S., Xiong, C., Bradbury, J., and Socher, R. Pointer sentinel mixture models, 2016

    2016

  32. [32]

    Aimo-2 winning solution: Building state- of-the-art mathematical reasoning models with openmathreasoning dataset

    Moshkov, I., Hanley, D., Sorokin, I., Toshniwal, S., Henkel, C., Schifferer, B., Du, W., and Gitman, I. Aimo-2 winning solution: Building state-of-the-art mathematical reasoning models with openmathreasoning dataset. arXiv preprint arXiv:2504.16891, 2025

    work page arXiv 2025

  33. [33]

    Large language diffusion models

    Nie, S., Zhu, F., You, Z., Zhang, X., Ou, J., Hu, J., Zhou, J., Lin, Y., Wen, J.-R., and Li, C. Large language diffusion models. In Neural Information Processing Systems, 2025 a

    2025

  34. [34]

    Large Language Diffusion Models

    Nie, S., Zhu, F., You, Z., Zhang, X., Ou, J., Hu, J., Zhou, J., Lin, Y., Wen, J.-R., and Li, C. Large language diffusion models. arXiv preprint arXiv:2502.09992, 2025 b

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  35. [35]

    Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data

    Ou, J., Nie, S., Xue, K., Zhu, F., Sun, J., Li, Z., and Li, C. Your absorbing discrete diffusion secretly models the conditional distributions of clean data. arXiv preprint arXiv:2406.03736, 2024

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  36. [36]

    The lambada dataset: Word prediction requiring a broad discourse context

    Paperno, D., Kruszewski, G., Lazaridou, A., Pham, N.-Q., Bernardi, R., Pezzelle, S., Baroni, M., Boleda, G., and Fern \'a ndez, R. The lambada dataset: Word prediction requiring a broad discourse context. In Proceedings of the 54th annual meeting of the association for computational linguistics (volume 1: Long papers), pp.\ 1525--1534, 2016

    2016

  37. [37]

    Language models are unsupervised multitask learners

    Radford, A., Wu, J., Child, R., Luan, D., Amodei, D., Sutskever, I., et al. Language models are unsupervised multitask learners. OpenAI blog, 1 0 (8): 0 9, 2019

    2019

  38. [38]

    Simple and effective masked diffusion language models

    Sahoo, S., Arriola, M., Schiff, Y., Gokaslan, A., Marroquin, E., Chiu, J., Rush, A., and Kuleshov, V. Simple and effective masked diffusion language models. Advances in Neural Information Processing Systems, 37: 0 130136--130184, 2024

    2024

  39. [39]

    Simplified and generalized masked diffusion for discrete data

    Shi, J., Han, K., Wang, Z., Doucet, A., and Titsias, M. Simplified and generalized masked diffusion for discrete data. Advances in neural information processing systems, 37: 0 103131--103167, 2024

    2024

  40. [40]

    Deep unsupervised learning using nonequilibrium thermodynamics

    Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N., and Ganguli, S. Deep unsupervised learning using nonequilibrium thermodynamics. In International conference on machine learning, pp.\ 2256--2265. pmlr, 2015

    2015

  41. [41]

    arXiv preprint arXiv:2211.04236 , year=

    Strudel, R., Tallec, C., Altch \'e , F., Du, Y., Ganin, Y., Mensch, A., Grathwohl, W., Savinov, N., Dieleman, S., Sifre, L., et al. Self-conditioned embedding diffusion for text generation. arXiv preprint arXiv:2211.04236, 2022

    work page arXiv 2022

  42. [42]

    arXiv preprint arXiv:2211.16750 , year=

    Sun, H., Yu, L., Dai, B., Schuurmans, D., and Dai, H. Score-based continuous-time discrete diffusion models. arXiv preprint arXiv:2211.16750, 2022

    work page arXiv 2022

  43. [43]

    arXiv preprint arXiv:2503.20853 (2025) 4

    Swerdlow, A., Prabhudesai, M., Gandhi, S., Pathak, D., and Fragkiadaki, K. Unified multimodal discrete diffusion. arXiv preprint arXiv:2503.20853, 2025

    work page arXiv 2025

  44. [44]

    LLaMA: Open and Efficient Foundation Language Models

    Touvron, H., Lavril, T., Izacard, G., Martinet, X., Lachaux, M.-A., Lacroix, T., Rozi \`e re, B., Goyal, N., Hambro, E., Azhar, F., et al. Llama: Open and efficient foundation language models. arXiv preprint arXiv:2302.13971, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  45. [45]

    Qwen2 Technical Report

    Yang, A., Yang, B., Hui, B., Zheng, B., Yu, B., Zhou, C., Li, C., Li, C., Liu, D., Huang, F., Dong, G., Wei, H., Lin, H., Tang, J., Wang, J., Yang, J., Tu, J., Zhang, J., Ma, J., Xu, J., Zhou, J., Bai, J., He, J., Lin, J., Dang, K., Lu, K., Chen, K.-Y., Yang, K., Li, M., Xue, M., Ni, N., Zhang, P., Wang, P., Peng, R., Men, R., Gao, R., Lin, R., Wang, S., ...

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  46. [46]

    MMaDA: Multimodal Large Diffusion Language Models

    Yang, L., Tian, Y., Li, B., Zhang, X., Shen, K., Tong, Y., and Wang, M. Mmada: Multimodal large diffusion language models. arXiv preprint arXiv:2505.15809, 2025

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  47. [47]

    Dream 7B: Diffusion Large Language Models

    Ye, J., Xie, Z., Zheng, L., Gao, J., Wu, Z., Jiang, X., Li, Z., and Kong, L. Dream 7b: Diffusion large language models. arXiv preprint arXiv:2508.15487, 2025

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  48. [48]

    Commonsense knowledge aware conversation generation with graph attention

    Zhou, H., Young, T., Huang, M., Zhao, H., Xu, J., and Zhu, X. Commonsense knowledge aware conversation generation with graph attention. In IJCAI, volume 18, pp.\ 4623--4629, 2018

    2018