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arxiv: 2606.00366 · v1 · pith:FDOV4RKCnew · submitted 2026-05-29 · 💻 cs.LG · math.OC

GLENS: Global Search via Learning from Solver Iterates with Diffusion Models

Anjian Li , Bartolomeo Stellato , Ryne Beeson This is my paper

Pith reviewed 2026-06-28 22:44 UTC · model grok-4.3

classification 💻 cs.LG math.OC
keywords diffusion modelsglobal optimizationinitial guessesnon-convex optimizationmultimodal problemssolver iteratesdata augmentationlocal minima
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The pith

Diffusion models trained on solver iterates generate high-quality diverse initial guesses for non-convex optimization.

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

The paper addresses generating many initial guesses for local minima in multimodal non-convex continuous optimization. Existing data-driven approaches train only on final converged solutions, which discards path information and limits data. GLENS instead treats all intermediate solver iterates as free augmentation to train diffusion models that capture local geometry around optima and solver refinement directions, conditioned on problem parameters. The resulting guesses remain diverse across modes yet close enough to optima that standard local solvers converge faster. This is shown on modified benchmark problems and a two-robot navigation task with obstacle avoidance.

Core claim

GLENS consists of a neighborhood structure model that uses diffusion models to learn the local geometry around optima conditioned on problem parameters, together with a solver behavior model that learns refinement directions; when these models generate new initial guesses from the distribution of iterates, the guesses preserve the multimodal distribution of local optima and produce faster convergence across solvers and problem instances.

What carries the argument

Two diffusion models trained on solver iterates: one modeling neighborhood structure around optima conditioned on problem parameters, the other modeling solver refinement directions to guide sampling.

If this is right

  • Generated initial guesses lead to faster convergence across different problem settings and solvers.
  • The multimodal distribution of diverse local optima is preserved rather than collapsed.
  • Using intermediate iterates as data augmentation makes training more data-efficient than methods that use only final solutions.
  • The approach applies to both modified non-convex benchmark problems and practical tasks such as two-robot obstacle-avoidance navigation.

Where Pith is reading between the lines

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

  • The same iterate-based training could be tested on iterative algorithms outside continuous optimization, such as iterative solvers in linear algebra or training loops in machine learning.
  • If the diffusion models scale, fewer total solver runs may be needed overall because each run starts closer to a distinct optimum.
  • Performance on problems with many more modes or higher dimension remains an open test of whether the learned local geometry generalizes.

Load-bearing premise

Intermediate solver iterates contain enough generalizable information about local neighborhoods around optima to train diffusion models that produce useful new guesses on unseen problem instances.

What would settle it

Run a local solver from GLENS-generated guesses versus from random starts or final-optima predictions on a held-out collection of multimodal problems and check whether convergence time or diversity of reached minima shows no improvement.

read the original abstract

We consider the problem of generating a large collection of initial guesses for local minima of multimodal non-convex continuous optimization problems. The goal is for these initial guesses to be high-quality (i.e., a numerical solver converges quickly) and diverse (i.e., represent many different local minima). Identifying multiple locally optimal solutions enables flexible downstream decision-making, but typically requires expensive global search. Existing data-driven methods predict initial guesses using only the final converged optima from offline solver runs, which discards information about the local neighborhoods of solutions and limits the available training data. We propose GLENS (Global Search via Learning from Solver Iterates), a data-efficient global search method that leverages intermediate solver iterates as free data augmentation. GLENS consists of two components: a neighborhood structure model that uses diffusion models to learn the local geometry around optima conditioned on problem parameters, and a solver behavior model that learns refinement directions to further guide samples towards nearby optima during diffusion sampling. Experiments on modified non-convex benchmark problems and a two-robot obstacle-avoidance navigation problem show that GLENS generates high-quality initial guesses while preserving the multimodal distribution of diverse local optima. The resulting initial guesses lead to faster solver convergence across different problem settings and solvers. We also analyze how key hyperparameter choices affect the performance.

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

1 major / 1 minor

Summary. The paper proposes GLENS, a data-efficient global search method for multimodal non-convex continuous optimization that trains diffusion models on intermediate solver iterates (rather than only final optima) to generate high-quality, diverse initial guesses. It consists of a neighborhood structure model (diffusion conditioned on problem parameters) and a solver behavior model (learning refinement directions). Experiments on modified non-convex benchmarks and a two-robot navigation task claim that the generated guesses preserve multimodal distributions and yield faster solver convergence across settings and solvers, with analysis of hyperparameter effects.

Significance. If the generalization from training iterates to unseen instances holds, the approach could meaningfully improve data efficiency for learning-based global optimization by treating solver trajectories as free augmentation, potentially benefiting applications like robotics and engineering design where multiple local optima must be identified. The use of diffusion models to capture local geometry around optima is a plausible extension of existing data-driven initialization methods.

major comments (1)
  1. [Experimental evaluation] Experimental evaluation (abstract and §4): the central claim that GLENS produces useful guesses for unseen problem instances requires evidence that the conditioned diffusion model generalizes beyond the training distribution of problem parameters. No held-out instance splits, parameter-space coverage metrics, or extrapolation tests are described, leaving open whether performance gains on the reported benchmarks and navigation task transfer when parameters differ in distribution from the offline runs used for training.
minor comments (1)
  1. [Abstract] The abstract states that GLENS 'preserves the multimodal distribution of diverse local optima' but does not specify quantitative metrics (e.g., diversity measures or mode coverage) used to support this.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the concern on experimental evaluation and generalization to unseen instances below.

read point-by-point responses

  1. Referee: [Experimental evaluation] Experimental evaluation (abstract and §4): the central claim that GLENS produces useful guesses for unseen problem instances requires evidence that the conditioned diffusion model generalizes beyond the training distribution of problem parameters. No held-out instance splits, parameter-space coverage metrics, or extrapolation tests are described, leaving open whether performance gains on the reported benchmarks and navigation task transfer when parameters differ in distribution from the offline runs used for training.

    Authors: We agree that explicit evidence of generalization is needed to support the central claim. Our experiments do vary problem parameters across benchmark instances (e.g., different coefficients and constraints in the modified non-convex functions) and use distinct obstacle configurations in the navigation task that were not part of the offline data collection runs. Nevertheless, the manuscript does not describe held-out instance splits, parameter-space coverage metrics, or dedicated extrapolation tests. In the revised version we will add a new subsection in §4 that (i) specifies the train/test splits over problem instances, (ii) reports coverage metrics on the parameter distributions, and (iii) includes additional results evaluating the diffusion model on parameter values outside the training range. These changes will directly address the referee’s concern. revision: yes

Circularity Check

0 steps flagged

No circularity; training on external solver iterates is independent of test predictions

full rationale

The paper trains diffusion models on intermediate solver iterates generated from offline runs on a set of problems, then uses the trained model to produce initial guesses for (modified) benchmark instances. This is a standard data-driven pipeline with no self-definitional reduction, no fitted parameter renamed as prediction, and no load-bearing self-citation chain. The derivation chain relies on external data generation and standard diffusion training, remaining self-contained against the target claim of improved guesses on new instances.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.1-grok · 5761 in / 924 out tokens · 18565 ms · 2026-06-28T22:44:10.996337+00:00 · methodology

discussion (0)

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Works this paper leans on

73 extracted references · 44 canonical work pages · 4 internal anchors

  1. [1]

    Advances in Neural Information Processing Systems37, 28706–28719 (2024) https://doi.org/10

    Dauner, D., Hallgarten, M., Li, T., Weng, X., Huang, Z., Yang, Z., Li, H., Gilitschenski, I., Ivanovic, B., Pavone, M.,et al.: NAVSIM: Data-driven non- reactive autonomous vehicle simulation and benchmarking. Advances in Neural Information Processing Systems37, 28706–28719 (2024) https://doi.org/10. 52202/079017-0902

    2024

  2. [2]

    Journal of Guidance, Control, and Dynamics40(1), 15–27 (2017) https://doi.org/10.2514/1.G002124

    Englander, J.A., Conway, B.A.: Automated solution of the low-thrust interplan- etary trajectory problem. Journal of Guidance, Control, and Dynamics40(1), 15–27 (2017) https://doi.org/10.2514/1.G002124

    work page doi:10.2514/1.g002124 2017

  3. [3]

    Annals of Operations Research240(1), 251–270 (2016) https://doi.org/10.1007/ s10479-015-2014-2

    Locatelli, M., Schoen, F.: Global optimization based on local searches. Annals of Operations Research240(1), 251–270 (2016) https://doi.org/10.1007/ s10479-015-2014-2

    2016

  4. [4]

    Journal of Global Optimization18(4), 367–383 (2000) https://doi.org/10.1023/A:1026500301312

    Leary, R.H.: Global optimization on funneling landscapes. Journal of Global Optimization18(4), 367–383 (2000) https://doi.org/10.1023/A:1026500301312

    work page doi:10.1023/a:1026500301312 2000

  5. [5]

    Foundations and Trends® in Machine Learning16(5), 592–732 (2023) https://doi.org/10.1561/2200000102

    Amos, B.,et al.: Tutorial on amortized optimization. Foundations and Trends® in Machine Learning16(5), 592–732 (2023) https://doi.org/10.1561/2200000102

    work page doi:10.1561/2200000102 2023

  6. [6]

    Automatica135, 109947 (2022) https://doi.org/10.1016/j.automatica.2021.109947

    Chen, S.W., Wang, T., Atanasov, N., Kumar, V., Morari, M.: Large scale model predictive control with neural networks and primal active sets. Automatica135, 109947 (2022) https://doi.org/10.1016/j.automatica.2021.109947

    work page doi:10.1016/j.automatica.2021.109947 2022

  7. [7]

    IEEE Robotics and Automation Letters7(2), 1447–1454 (2021) https://doi.org/10.1109/LRA

    Cauligi, A., Culbertson, P., Schmerling, E., Schwager, M., Stellato, B., Pavone, M.: CoCo: Online mixed-integer control via supervised learning. IEEE Robotics and Automation Letters7(2), 1447–1454 (2021) https://doi.org/10.1109/LRA. 2021.3135931

    work page doi:10.1109/lra 2021

  8. [8]

    Machine Learning110(2), 249–277 (2021) https://doi.org/10.1007/s10994-020-05893-5

    Bertsimas, D., Stellato, B.: The voice of optimization. Machine Learning110(2), 249–277 (2021) https://doi.org/10.1007/s10994-020-05893-5

    work page doi:10.1007/s10994-020-05893-5 2021

  9. [9]

    Journal of Machine Learning Research25(166), 1–46 (2024)

    Sambharya, R., Hall, G., Amos, B., Stellato, B.: Learning to warm-start fixed- point optimization algorithms. Journal of Machine Learning Research25(166), 1–46 (2024)

    2024

  10. [10]

    Advances in neural information processing systems32(2019) 32

    Song, Y., Ermon, S.: Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems32(2019) 32

    2019

  11. [11]

    Advances in neural information processing systems33, 6840–6851 (2020)

    Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Advances in neural information processing systems33, 6840–6851 (2020)

    2020

  12. [12]

    Advances in neural information processing systems36, 3706–3731 (2023)

    Sun, Z., Yang, Y.: DIFUSCO: Graph-based diffusion solvers for combinatorial optimization. Advances in neural information processing systems36, 3706–3731 (2023)

    2023

  13. [13]

    In: Proceedings of the 7th Annual Learning for Dynamics & Control Conference

    Li, A., Ding, Z., Dieng, A.B., Beeson, R.: DiffuSolve: Diffusion-based solver for non-convex trajectory optimization. In: Proceedings of the 7th Annual Learning for Dynamics & Control Conference. Proceedings of Machine Learning Research, vol. 283, pp. 45–58 (2025). PMLR

    2025

  14. [14]

    Journal of the Astronautical Sciences72(6), 62 (2025) https://doi.org/10.1007/s40295-025-00535-1

    Graebner, J., Beeson, R.: Global search for optimal low thrust spacecraft trajecto- ries using diffusion models and the indirect method. Journal of the Astronautical Sciences72(6), 62 (2025) https://doi.org/10.1007/s40295-025-00535-1

    work page doi:10.1007/s40295-025-00535-1 2025

  15. [15]

    arXiv preprint arXiv:2412.20023 (2024) https://doi.org/10.48550/arXiv.2412.20023

    Beeson, R., Li, A., Sinha, A.: Global search of optimal spacecraft trajectories using amortization and deep generative models. arXiv preprint arXiv:2412.20023 (2024) https://doi.org/10.48550/arXiv.2412.20023

    work page doi:10.48550/arxiv.2412.20023 2024

  16. [16]

    In: Blasch, E., Darema, F., Metaxas, D

    Li, A., Ding, Z., Dieng, A.B., Beeson, R.: Constraint-aware diffusion models for trajectory optimization. In: Blasch, E., Darema, F., Metaxas, D. (eds.) Dynamic Data Driven Applications Systems, pp. 308–316. Springer, Cham (2026). https: //doi.org/10.1007/978-3-031-94895-4 32

    work page doi:10.1007/978-3-031-94895-4 2026

  17. [17]

    In: Blasch, E., Darema, F., Metaxas, D

    Li, A., Beeson, R.: Aligning diffusion model with problem constraints for tra- jectory optimization. In: Blasch, E., Darema, F., Metaxas, D. (eds.) Handbook of Dynamic Data-Driven Applications Systems vol. 4. Springer, Cham (2025). https://doi.org/10.48550/arXiv.2504.00342

    work page doi:10.48550/arxiv.2504.00342 2025

  18. [18]

    SIAM Journal on scientific computing16(5), 1190–1208 (1995) https://doi.org/10.1137/0916069

    Byrd, R.H., Lu, P., Nocedal, J., Zhu, C.: A limited memory algorithm for bound constrained optimization. SIAM Journal on scientific computing16(5), 1190–1208 (1995) https://doi.org/10.1137/0916069

    work page doi:10.1137/0916069 1995

  19. [19]

    SIAM review47(1), 99–131 (2005) https://doi

    Gill, P.E., Murray, W., Saunders, M.A.: SNOPT: An SQP algorithm for large- scale constrained optimization. SIAM review47(1), 99–131 (2005) https://doi. org/10.1137/S0036144504446096

    work page doi:10.1137/s0036144504446096 2005

  20. [20]

    Scientific american267(1), 66–72 (1992) https: //doi.org/10.1038/scientificamerican0792-66

    Holland, J.H.: Genetic algorithms. Scientific american267(1), 66–72 (1992) https: //doi.org/10.1038/scientificamerican0792-66

    work page doi:10.1038/scientificamerican0792-66 1992

  21. [21]

    Journal of global optimization11(4), 341–359 (1997) https://doi.org/10.1023/A:1008202821328

    Storn, R., Price, K.: Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of global optimization11(4), 341–359 (1997) https://doi.org/10.1023/A:1008202821328

    work page doi:10.1023/a:1008202821328 1997

  22. [22]

    In: Proceedings of ICNN’95-international Conference on Neural Networks, vol

    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN’95-international Conference on Neural Networks, vol. 4, pp. 1942–1948 33 (1995). https://doi.org/10.1109/ICNN.1995.488968 . IEEE

    work page doi:10.1109/icnn.1995.488968 1942

  23. [23]

    In: Astrodynamics Conference, p

    Cage, P., Kroo, I., Braun, R.: Interplanetary trajectory optimization using a genetic algorithm. In: Astrodynamics Conference, p. 3773 (1994). https://doi. org/10.2514/6.1994-3773

    work page doi:10.2514/6.1994-3773 1994

  24. [24]

    Journal of Spacecraft and Rockets39(6), 859–865 (2002) https://doi.org/ 10.2514/2.3908

    Kim, Y.H., Spencer, D.B.: Optimal spacecraft rendezvous using genetic algo- rithms. Journal of Spacecraft and Rockets39(6), 859–865 (2002) https://doi.org/ 10.2514/2.3908

    work page doi:10.2514/2.3908 2002

  25. [25]

    Journal of Spacecraft and Rockets44(5), 1060–1070 (2007) https://doi.org/10.2514/1.27242

    Olds, A.D., Kluever, C.A., Cupples, M.L.: Interplanetary mission design using differential evolution. Journal of Spacecraft and Rockets44(5), 1060–1070 (2007) https://doi.org/10.2514/1.27242

    work page doi:10.2514/1.27242 2007

  26. [26]

    Journal of Global Optimization38(2), 283–296 (2007) https://doi.org/10.1007/ s10898-006-9106-0

    Izzo, D., Becerra, V.M., Myatt, D.R., Nasuto, S.J., Bishop, J.M.: Search space pruning and global optimisation of multiple gravity assist spacecraft trajectories. Journal of Global Optimization38(2), 283–296 (2007) https://doi.org/10.1007/ s10898-006-9106-0

    2007

  27. [27]

    arithmetic circuits: A case study

    Miller, J.F., Thomson, P., Fogarty, T., et al.: Designing electronic circuits using evolutionary algorithms. arithmetic circuits: A case study. Genetic algorithms and evolution strategies in engineering and computer science10(1997)

    1997

  28. [28]

    Analog integrated circuits and signal processing63(1), 71–82 (2010) https://doi.org/10

    Fakhfakh, M., Cooren, Y., Sallem, A., Loulou, M., Siarry, P.: Analog circuit design optimization through the particle swarm optimization technique. Analog integrated circuits and signal processing63(1), 71–82 (2010) https://doi.org/10. 1007/s10470-009-9361-3

    2010

  29. [29]

    In: Proceedings of the 6th International Conference on Genetic Algorithms, pp

    Kobayashi, S., Ono, I., Yamamura, M.: An efficient genetic algorithm for job shop scheduling problems. In: Proceedings of the 6th International Conference on Genetic Algorithms, pp. 506–511 (1995)

    1995

  30. [30]

    Computers & operations research35(10), 3202–3212 (2008) https://doi.org/10.1016/j.cor.2007.02.014

    Pezzella, F., Morganti, G., Ciaschetti, G.: A genetic algorithm for the flexible job- shop scheduling problem. Computers & operations research35(10), 3202–3212 (2008) https://doi.org/10.1016/j.cor.2007.02.014

    work page doi:10.1016/j.cor.2007.02.014 2008

  31. [31]

    INFORMS Journal on computing19(3), 328–340 (2007) https://doi.org/10.1287/ijoc.1060

    Ugray, Z., Lasdon, L., Plummer, J., Glover, F., Kelly, J., Mart´ ı, R.: Scatter search and local nlp solvers: A multistart framework for global optimization. INFORMS Journal on computing19(3), 328–340 (2007) https://doi.org/10.1287/ijoc.1060. 0175

    work page doi:10.1287/ijoc.1060 2007

  32. [32]

    The Jour- nal of Physical Chemistry A101(28), 5111–5116 (1997) https://doi.org/10.1021/ jp970984n

    Wales, D.J., Doye, J.P.: Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 atoms. The Jour- nal of Physical Chemistry A101(28), 5111–5116 (1997) https://doi.org/10.1021/ jp970984n

    1997

  33. [33]

    Journal of chemical information and modeling53(9), 2282–2298 (2013) https://doi.org/10.1021/ ci400224z

    Rondina, G.G., Da Silva, J.L.: Revised basin-hopping monte carlo algorithm 34 for structure optimization of clusters and nanoparticles. Journal of chemical information and modeling53(9), 2282–2298 (2013) https://doi.org/10.1021/ ci400224z

    2013

  34. [34]

    Spatially Resolving Electron Spin Resonance ofπ-Radical in Single-Molecule Magnet

    Banerjee, A., Jasrasaria, D., Niblett, S.P., Wales, D.J.: Crystal structure pre- diction for benzene using basin-hopping global optimization. The Journal of Physical Chemistry A125(17), 3776–3784 (2021) https://doi.org/10.1021/acs. jpca.1c00903

    work page doi:10.1021/acs 2021

  35. [35]

    Bioinformatics 30(14), 2009–2017 (2014) https://doi.org/10.1093/bioinformatics/btu156

    Kucharik, M., Hofacker, I.L., Stadler, P.F., Qin, J.: Basin hopping graph: a computational framework to characterize rna folding landscapes. Bioinformatics 30(14), 2009–2017 (2014) https://doi.org/10.1093/bioinformatics/btu156

    work page doi:10.1093/bioinformatics/btu156 2009

  36. [36]

    The Journal of chemical physics128(22) (2008) https://doi.org/ 10.1063/1.2929833

    Prentiss, M.C., Wales, D.J., Wolynes, P.G.: Protein structure prediction using basin-hopping. The Journal of chemical physics128(22) (2008) https://doi.org/ 10.1063/1.2929833

    work page doi:10.1063/1.2929833 2008

  37. [37]

    In: 2018 Space Flight Mechanics Meeting, p

    McCarty, S.L., Burke, L.M., McGuire, M.: Parallel monotonic basin hopping for low thrust trajectory optimization. In: 2018 Space Flight Mechanics Meeting, p. 1452 (2018). https://doi.org/10.2514/6.2018-1452

    work page doi:10.2514/6.2018-1452 2018

  38. [38]

    Journal of Spacecraft and Rockets47(2), 334–344 (2010) https://doi.org/10.2514/1.45742

    Vasile, M., Minisci, E., Locatelli, M.: Analysis of some global optimization algo- rithms for space trajectory design. Journal of Spacecraft and Rockets47(2), 334–344 (2010) https://doi.org/10.2514/1.45742

    work page doi:10.2514/1.45742 2010

  39. [39]

    In: 2019 American Control Conference (ACC), pp

    Zhang, X., Bujarbaruah, M., Borrelli, F.: Safe and near-optimal policy learning for model predictive control using primal-dual neural networks. In: 2019 American Control Conference (ACC), pp. 354–359 (2019). https://doi.org/10.23919/ACC. 2019.8814335 . IEEE

    work page doi:10.23919/acc 2019

  40. [40]

    Journal of Global Optimization91(1), 1–37 (2025) https://doi.org/10.1007/ s10898-024-01434-9

    Bertsimas, D., Margaritis, G.: Global optimization: a machine learning approach. Journal of Global Optimization91(1), 1–37 (2025) https://doi.org/10.1007/ s10898-024-01434-9

    2025

  41. [41]

    Advances in Neural Information Processing Systems36, 50020–50040 (2023)

    Li, Y., Guo, J., Wang, R., Yan, J.: T2t: From distribution learning in training to gradient search in testing for combinatorial optimization. Advances in Neural Information Processing Systems36, 50020–50040 (2023)

    2023

  42. [42]

    Computational Optimization and Applications 51(1), 279–303 (2012) https://doi.org/10.1007/s10589-010-9330-x

    Cassioli, A., Di Lorenzo, D., Locatelli, M., Schoen, F., Sciandrone, M.: Machine learning for global optimization. Computational Optimization and Applications 51(1), 279–303 (2012) https://doi.org/10.1007/s10589-010-9330-x

    work page doi:10.1007/s10589-010-9330-x 2012

  43. [43]

    In: AAS/AIAA Astrodynamics Specialist Conference (2023)

    Li, A., Sinha, A., Beeson, R.: Amortized global search for efficient preliminary trajectory design with deep generative models. In: AAS/AIAA Astrodynamics Specialist Conference (2023). https://doi.org/10.48550/arXiv.2308.03960 35

    work page doi:10.48550/arxiv.2308.03960 2023

  44. [44]

    arXiv preprint arXiv:2411.02158 (2024) https://doi.org/10.48550/arXiv.2411.02158

    Sharony, E., Yang, H., Che, T., Pavone, M., Mannor, S., Karkus, P.: Learning mul- tiple initial solutions to optimization problems. arXiv preprint arXiv:2411.02158 (2024) https://doi.org/10.48550/arXiv.2411.02158

    work page doi:10.48550/arxiv.2411.02158 2024

  45. [45]

    In: AAS/AIAA Astrodynamics Specialist Conference (2024)

    Graebner, J., Li, A., Sinha, A., Beeson, R.: Learning optimal control and dynamical structure of global trajectory search problems with diffusion models. In: AAS/AIAA Astrodynamics Specialist Conference (2024). https://doi.org/10. 48550/arXiv.2410.02976

    arXiv 2024

  46. [46]

    In: First International Conference on Informatics in Control, Automation and Robotics, vol

    Li, W., Todorov, E.: Iterative linear quadratic regulator design for nonlinear bio- logical movement systems. In: First International Conference on Informatics in Control, Automation and Robotics, vol. 2, pp. 222–229 (2004). SciTePress

    2004

  47. [47]

    Advances in neural information processing systems36, 51830–51861 (2023)

    Giannone, G., Srivastava, A., Winther, O., Ahmed, F.: Aligning optimization trajectories with diffusion models for constrained design generation. Advances in neural information processing systems36, 51830–51861 (2023)

    2023

  48. [48]

    In: International Confer- ence on Machine Learning, pp

    Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N., Ganguli, S.: Deep unsuper- vised learning using nonequilibrium thermodynamics. In: International Confer- ence on Machine Learning, pp. 2256–2265 (2015). pmlr

    2015

  49. [49]

    GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models

    Nichol, A., Dhariwal, P., Ramesh, A., Shyam, P., Mishkin, P., McGrew, B., Sutskever, I., Chen, M.: GLIDE: Towards photorealistic image generation and editing with text-guided diffusion models. arXiv preprint arXiv:2112.10741 (2021) https://doi.org/10.48550/arXiv.2112.10741

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2112.10741 2021

  50. [50]

    Masked Autoencoders Are Scalable Vision Learners,

    Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 10684–10695 (2022). https://doi.org/10.1109/CVPR52688.2022.01042

    work page doi:10.1109/cvpr52688.2022.01042 2022

  51. [51]

    Advances in neural information processing systems35, 8633– 8646 (2022)

    Ho, J., Salimans, T., Gritsenko, A., Chan, W., Norouzi, M., Fleet, D.J.: Video diffusion models. Advances in neural information processing systems35, 8633– 8646 (2022)

    2022

  52. [52]

    arXiv preprint arXiv:2304.02198 (2023) https://doi.org/10.48550/arXiv.2304.02198

    Jing, B., Erives, E., Pao-Huang, P., Corso, G., Berger, B., Jaakkola, T.: EigenFold: Generative protein structure prediction with diffusion models. arXiv preprint arXiv:2304.02198 (2023) https://doi.org/10.48550/arXiv.2304.02198

    work page doi:10.48550/arxiv.2304.02198 2023

  53. [53]

    Nature communications15(1), 1059 (2024) https://doi.org/10.1038/s41467-024-45051-2

    Wu, K.E., Yang, K.K., Berg, R., Alamdari, S., Zou, J.Y., Lu, A.X., Amini, A.P.: Protein structure generation via folding diffusion. Nature communications15(1), 1059 (2024) https://doi.org/10.1038/s41467-024-45051-2

    work page doi:10.1038/s41467-024-45051-2 2024

  54. [54]

    Nature Computational Science4(12), 899–909 (2024) https://doi.org/10.1038/s43588-024-00737-x 36

    Schneuing, A., Harris, C., Du, Y., Didi, K., Jamasb, A., Igashov, I., Du, W., Gomes, C., Blundell, T.L., Lio, P.,et al.: Structure-based drug design with equiv- ariant diffusion models. Nature Computational Science4(12), 899–909 (2024) https://doi.org/10.1038/s43588-024-00737-x 36

    work page doi:10.1038/s43588-024-00737-x 2024

  55. [55]

    Planning with Diffusion for Flexible Behavior Synthesis

    Janner, M., Du, Y., Tenenbaum, J.B., Levine, S.: Planning with diffusion for flexible behavior synthesis. arXiv preprint arXiv:2205.09991 (2022) https://doi. org/10.48550/arXiv.2205.09991

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2205.09991 2022

  56. [56]

    Ajay, A., Du, Y., Gupta, A., Tenenbaum, J., Jaakkola, T., Agrawal, P.: Is con- ditional generative modeling all you need for decision-making? arXiv preprint arXiv:2211.15657 (2022) https://doi.org/10.48550/arXiv.2211.15657

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2211.15657 2022

  57. [57]

    The International Journal of Robotics Research44(10-11), 1684–1704 (2025) https: //doi.org/10.1177/02783649241273668

    Chi, C., Xu, Z., Feng, S., Cousineau, E., Du, Y., Burchfiel, B., Tedrake, R., Song, S.: Diffusion Policy: Visuomotor policy learning via action diffusion. The International Journal of Robotics Research44(10-11), 1684–1704 (2025) https: //doi.org/10.1177/02783649241273668

    work page doi:10.1177/02783649241273668 2025

  58. [58]

    10 TRACER: Persistent Regularization for Robust Multimodal Finetuning Fang, A., Jose, A

    Jiang, C., Cornman, A., Park, C., Sapp, B., Zhou, Y., Anguelov, D.,et al.: MotionDiffuser: Controllable multi-agent motion prediction using diffusion. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9644–9653 (2023). https://doi.org/10.1109/CVPR52729.2023. 00930

    work page doi:10.1109/cvpr52729.2023 2023

  59. [59]

    a fer, Andrew Wing Keung To, Kuan-Ho Lao, Murat Cubuktepe, Matthew Haley, Peter B \

    Zhang, Z., Li, A., Lim, A., Chen, M.: Predicting long-term human behaviors in discrete representations via physics-guided diffusion. In: 2024 IEEE/RSJ Inter- national Conference on Intelligent Robots and Systems (IROS), pp. 11500–11507 (2024). https://doi.org/10.1109/IROS58592.2024.10802068 . IEEE

    work page doi:10.1109/iros58592.2024.10802068 2024

  60. [60]

    In: IEEE International Conference on Intelligent Transportation Systems (ITSC) (2025)

    Li, A., Bae, S., Isele, D., Beeson, R., Tariq, F.M.: Predictive planner for autonomous driving with consistency models. In: IEEE International Conference on Intelligent Transportation Systems (ITSC) (2025). https://doi.org/10.48550/ arXiv.2502.08033

    arXiv 2025

  61. [61]

    Classifier-Free Diffusion Guidance

    Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) https://doi.org/10.48550/arXiv.2207.12598

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2207.12598 2022

  62. [62]

    Advances in neural information processing systems34, 8780–8794 (2021)

    Dhariwal, P., Nichol, A.: Diffusion models beat gans on image synthesis. Advances in neural information processing systems34, 8780–8794 (2021)

    2021

  63. [63]

    U-net: Convolutional networks for biomedical image segmentation

    Ronneberger, O., Fischer, P., Brox, T.: U-Net: Convolutional networks for biomedical image segmentation. In: International Conference on Medical Image Computing and Computer-assisted Intervention, pp. 234–241 (2015). https://doi. org/10.1007/978-3-319-24574-4 28 . Springer

    work page doi:10.1007/978-3-319-24574-4 2015

  64. [64]

    Advances in neural information processing systems30(2017)

    Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, L., Polosukhin, I.: Attention is all you need. Advances in neural information processing systems30(2017)

    2017

  65. [65]

    URL http://proceedings

    Peebles, W., Xie, S.: Scalable diffusion models with transformers. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 4195–4205 (2023). https://doi.org/10.1109/ICCV51070.2023.00387 37

    work page doi:10.1109/iccv51070.2023.00387 2023

  66. [66]

    (eds.) Nonlinear Programming, pp

    Kuhn, H.W., Tucker, A.W.: In: Giorgi, G., Kjeldsen, T.H. (eds.) Nonlinear Programming, pp. 247–258. Springer, Basel (2014). https://doi.org/10.1007/ 978-3-0348-0439-4 11

    2014

  67. [67]

    (lucidrains), P.W.: denoising-diffusion-pytorch: Implementation of Denoising Dif- fusion Probabilistic Model in PyTorch. GitHub. Accessed: 2026-01-10 (2025)

    2026

  68. [68]

    McGraw-Hill, New York (1972)

    Himmelblau, D.M.: Applied Nonlinear Programming. McGraw-Hill, New York (1972)

    1972

  69. [69]

    Nature Methods17, 261–272 (2020) https://doi.org/10.1038/ s41592-019-0686-2

    Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Courna- peau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, ˙I., Feng, Y., Moore, E.W., Vander- Plas, J., Laxalde, D., Perktold, J., Ci...

    2020

  70. [70]

    The computer journal3(3), 175–184 (1960) https://doi.org/10.1093/ comjnl/3.3.175

    Rosenbrock, H.H.: An automatic method for finding the greatest or least value of a function. The computer journal3(3), 175–184 (1960) https://doi.org/10.1093/ comjnl/3.3.175

    1960

  71. [71]

    Journal of Optimization Theory and Applications80(1), 175–179 (1994) https: //doi.org/10.1007/BF02196600

    Dixon, L., Mills, D.: Effect of rounding errors on the variable metric method. Journal of Optimization Theory and Applications80(1), 175–179 (1994) https: //doi.org/10.1007/BF02196600

    work page doi:10.1007/bf02196600 1994

  72. [72]

    Journal of Global Optimization 33(2), 235–255 (2005) https://doi.org/10.1007/s10898-004-1936-z

    Laguna, M., Marti, R.: Experimental testing of advanced scatter search designs for global optimization of multimodal functions. Journal of Global Optimization 33(2), 235–255 (2005) https://doi.org/10.1007/s10898-004-1936-z

    work page doi:10.1007/s10898-004-1936-z 2005

  73. [73]

    Journal of Open Source Software5(54), 2564 (2020) https://doi.org/10

    Wu, E., Kenway, G., Mader, C.A., Jasa, J., Martins, J.R.R.A.: pyOptSparse: A python framework for large-scale constrained nonlinear optimization of sparse systems. Journal of Open Source Software5(54), 2564 (2020) https://doi.org/10. 21105/joss.02564 38

    2020