IDEQ -- Improving Diffusion Models for the Traveling Salesman Problem (TSP) by Leveraging the Structure of the Solution Space

Mickael Basson; Philippe Preux

REVIEW 2 major objections 6 minor 33 references

IDEQ -- Improving Diffusion Models for the Traveling Salesman Problem (TSP) by Leveraging the Structure of the Solution Space

T0 review · 2 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read IDEQ, a diffusion-based neural solver for the TSP, enforces Hamiltonian structure at every denoising step and retrains on the 2-opt equivalence class of optimal tours, reaching 0.3% optimality gap at 500 cities and beating LKH3 on two…

desk verdict Strong empirical results for a diffusion-based TSP solver, but the paper's headline mechanism — a uniform distribution over 2-opt orbits — is not actually implemented; the numbers still deserve a serious look. read the letter →

arxiv 2412.13858 v2 pith:T2DAYDKX submitted 2024-12-18 cs.AI cs.LG

Mickael Basson , Philippe Preux This is my paper · ORCID

classification cs.AIcs.LG MSC 90C2768T0705C45

keywords diffusionmodelstravelingsalesmanproblemcombinatorialoptimization2-optHamiltoniantourscurriculumlearningTSPlibneuralsolvers

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes IDEQ, a diffusion-model solver for the Euclidean Traveling Salesman Problem that improves on the DIFUSCO and T2TCO lines of work. Its first ingredient constrains the reverse diffusion: every predicted adjacency matrix is passed through a Hamiltonian-tour reconstruction operator and then refined by one 2-opt step, so the model never samples an invalid tour. Its second ingredient changes the training objective in the later curriculum stages: instead of teaching the network a single optimal tour per instance, IDEQ labels each instance with tours obtained by two random 2-changes from the optimum, i.e. members of the equivalence class of tours that 2-opt collapses to the optimum. On random instances IDEQ reports a 0.3% optimality gap (excess tour length over the optimum) at 500 cities and 0.5% at 1,000 cities, which the paper counts as a new state of the art for neural methods, and on TSPlib it is close to LKH3, finding shorter tours than LKH3 on instances fl1577 and fl3795.

What carries the argument

The load-bearing object is the 2-opt equivalence relation on Hamiltonian tours: two tours are equivalent when repeated applications of the 2-opt operator send one to the other, and every locally optimal tour is a fixed point of that operator. IDEQ uses this relation in two places: at inference, the operator $R_2 \circ H$ is applied at every reverse-diffusion step to guarantee Hamiltonian validity and local improvement; at training, two random 2-change moves from the optimal tour generate labels from the equivalence class, so the network learns a distribution over many tours that all collapse to the optimum. The argument works because the inference projection changes only the estimator of $x_0$ and not the training loss, so existing DIFUSCO checkpoints can be fine-tuned rather than retrained from scratch.

What would settle it

Retrain the same IDEQ pipeline with labels drawn from a longer random walk in the 2-opt equivalence class instead of only two 2-changes; if the optimality gaps stay unchanged, the equivalence-class objective is not what causes the improvement, and if they improve, the two-change sampler is leaving performance unused.

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Extended reading notes

Core claim

The central claim is that a diffusion model for the TSP becomes markedly better when the solution-space geometry is respected in both directions of the process. During generation, the standard denoising step is replaced by the composition $\hat{x}_0 = R_2 \circ H \circ NN_\theta(x_t, t, I)$, where $H$ reconstructs a Hamiltonian tour from the predicted heatmap and $R_2$ applies 2-opt; because an optimal tour is a fixed point of 2-opt, this projection lets every intermediate prediction remain a genuine tour and pushes the walk toward locally optimal adjacency structures. During training, the one-point target distribution on the optimal tour is replaced by a uniform distribution over its 2-opt equivalence class, implemented by sampling two random 2-changes from the optimal tour as the label. The authors argue that this enlarges the support of the target distribution, making the learned denoiser more robust, and their experiments attribute the final gap reduction to the two ingredients adding up independently.

Load-bearing premise

The retraining gain rests on the assumption that sampling two random 2-changes from the optimal tour is a faithful enough stand-in for a uniform distribution over the whole 2-opt equivalence class of that tour.

Editorial extensions

If this is right

If the reported gaps hold, a neural diffusion solver with 2-opt post-processing becomes the first neural method effectively competing with LKH3-class heuristics on structured TSP instances with thousands of cities.
The gains come from fine-tuning existing DIFUSCO checkpoints with a modified objective, not from training a new diffusion model from scratch, so the improvement is comparatively cheap.
The two ingredients are additive: the ablation study shows that inference-time projection and equivalence-class retraining each improve T2TCO, and combining them yields IDEQ.
Because optimal tours are 2-opt fixed points, the same equivalence-class retraining recipe transfers to other combinatorial problems that admit a similar invertible local transformation.
Reduced variance across repeated solves indicates that constraining the search space makes the denoising process less sensitive to the initial random noise.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A consequence the authors leave implicit is that the practical value of the diffusion model may lie mainly in producing a good starting tour for local search: iterating 2-opt from a random Hamiltonian tour alone leaves gaps of a few percent, so the diffusion component is what makes the small final gaps possible.
The sampler uses only two random 2-changes per label rather than the full uniform distribution over the equivalence class; testing longer random walks in the class would show whether the reported gains track the intended objective or merely the diversity of a few nearby tours.
The LKH3 comparisons use default solver settings, so a natural extension is to measure how much of the two 'wins' survives when LKH3 is tuned for those specific instances.
The recipe's applicability claim suggests a concrete test: apply the same constrained-diffusion plus equivalence-class fine-tuning to vehicle routing or maximum cut, where the corresponding local-search operator plays the role of 2-opt.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

You should know about this paper because it reports the strongest numbers yet for a neural diffusion solver on the TSP: 0.29% gap on TSP-500 and 0.49% on TSP-1000 with sampling, beating T2TCO by a wide margin, and the first reported case of a neural method beating LKH3 on two TSPlib instances. The ablation study is real and separates the two ingredients. If those numbers are reproducible, this is a meaningful step for neural combinatorial optimization.

What is genuinely new is the combination: (1) injecting a Hamiltonian reconstruction and 2-opt into the diffusion inference loop, and (2) fine-tuning the later curriculum stages on optimal tours perturbed by two random 2-changes. The first ingredient is in the spirit of the usual post-processing, but applying it inside the iterative denoising is a concrete change. The second is essentially a data augmentation trick, but the empirical gain is substantial and the authors show it is independent of the inference change.

The soft spots are in the framing. The abstract says the retraining objective is a uniform distribution over Hamiltonian tours whose orbits by 2-opt converge to the optimal tour. That is not what is implemented: Section 3.3 literally says "we use only 2 applications of 2-change." Two random 2-changes do not uniformly sample the equivalence class, and there is no argument that they avoid the local minima the paper itself warns about. So the reported gains cannot be attributed to the equivalence-class objective. The gains may come from label smoothing, increased diversity, or simply providing tours that 2-opt can repair — all plausible, but unidentified. This is an attribution problem, not a falsification of the numbers.

The paper also makes a strong claim that T2TCO's gradient search is not responsible for its improvement, but gives no quantitative support. And the statement in Section 3.2 that the reconstruction operator leaves the optimal theta unchanged is confusing — you are not training with that operator, so the point is moot.

Who should read this? Anyone working on neural TSP or diffusion for combinatorial optimization. It is a solid empirical paper with a clear ablation, but the methodological story needs rewriting. I would send it under conditional acceptance with a demand to either fix the description or provide evidence that the approximation captures the intended distribution.

Regards.

Referee Report

2 major / 6 minor

Summary. The paper proposes IDEQ, a discrete diffusion model for the Euclidean TSP built on DIFUSCO and T2TCO. IDEQ introduces two modifications: at inference time, the denoising process is guided by applying a Hamiltonian reconstruction operator followed by 2-opt at every reverse step (Section 3.2); and at training time, the later curriculum stages are fine-tuned with a target distribution that, according to the paper, is uniform over the equivalence class of the optimal tour under the 2-opt operator, but is implemented by applying two random 2-change perturbations to the optimal tour (Sections 3.3 and 3.4). Experiments on random TSP-500 and TSP-1000 instances and on TSPlib report improved optimality gaps over DIFUSCO and T2TCO, with gaps of 0.3% and 0.5% respectively, and on two TSPlib instances the method finds tours shorter than the LKH3 reference.

Significance. If the reported results are reproducible, the paper would be a meaningful step for neural TSP solvers: it demonstrates that a diffusion model with 2-opt post-processing can approach the solution quality of classical heuristics on structured instances, and the larger test set and re-run baselines strengthen the empirical comparison. The ablation study (Table 4) attempts to separate the contributions of the two ingredients, which is commendable. However, the stated methodological novelty of ingredient 2 is not actually what is implemented, so the attribution of the gains to the uniform-orbit objective is unsupported. The empirical central claim is plausible but the paper needs either a corrected implementation or a revised claim and analysis.

major comments (2)

[Section 3.3 and Section 3.4] The training objective is stated as a uniform distribution over the equivalence class of the optimal tour under the 2-opt operator R2, but the implementation samples tours by applying two randomly chosen 2-change moves to the optimal tour. A 2-change is a single edge-exchange move, while R2 in Section 2.1 is the local-search operator that repeatedly applies the most length-decreasing 2-change until a local optimum; a tour obtained from two random 2-changes need not lie in the equivalence class from which R2 converges to the optimum, and the text itself acknowledges that inverting 2-changes can generate local minima. The claim in Section 3.3 that this 'creates a set of diverse members of the equivalence class' is therefore unsupported. Because this objective is the core of key ingredient 2, the improvements in Table 4 cannot be attributed to the stated uniform-orbit target; they may result from label smoothing or from training the model to produce tours that 2-opt can repair. The authors should either implement the actual uniform sampling over the equivalence class or reframe the method as an approximate label augmentation with an explicit justification and an analysis of the bias it introduces.
[Section 3.3] The sentence 'while creating O(N−1) local minimal which is at least one order of magnitude lower than the number of epoches for TSP instance ≥ 500 as considered here' is incomplete and does not provide an argument for the adequacy of the two-2-change approximation. It does not define what quantity is O(N−1), how the number of local minima is counted, or why comparing it with the number of training epochs is relevant to whether the sampled set is representative of the equivalence class. This is load-bearing because it is the only justification offered for replacing the uniform distribution by two random 2-changes; please replace it with a precise statement, ideally with a formal or empirical analysis of the distance between the implemented label distribution and the claimed uniform distribution.

minor comments (6)

[Section 1] The phrase 'up to a 7397 cities' should read 'up to 7,397 cities'.
[Table 2] The header '100- 104' is ambiguous; it should be '100 to 10^4' or similar.
[Sections 2.2 and 2.3] There are missing citations indicated by '[?]' (for example, 'and further expanded by various authors [5, 26, 20, ?]' and in the reference list); these should be completed.
[Section 4.3 and Appendix A] The term 'optimality gap' is used for comparisons against LKH3 reference tours; for fl1577 and fl3795 the reported gaps are negative. Please state explicitly that these gaps are relative to the LKH3 reference (default settings) rather than to a proven optimum, to avoid confusing readers.
[Section 4.4, Table 4] The reported running times for the IDEQ rows appear inconsistent with Table 1: IDEQ 0.41% is paired with 3.7 mn in Table 4 but with 1.3 mn in Table 1 for the non-sampling configuration, and similar discrepancies appear for TSP-1000. Please check and correct these entries.
[Section 2.3] The claim that T2TCO's gradient-based search is not responsible for its improvement is stated without experimental support; since this motivates the IDEQ inference design, a brief description of the experiment would strengthen the paper.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: IDEQ's reported gains are benchmarked against external exact/heuristic solvers, and the 2-change training-target approximation is an implementation mismatch, not a circular reduction.

full rationale

IDEQ's central empirical claims are not forced by construction. The TSP-500/TSP-1000 optimality gaps and TSPlib tour lengths are compared against Concorde (exact solver) and LKH3 (external heuristic), not against quantities fitted from the model itself. The two claimed ingredients are independently ablated in Table 4: using the IDEQ checkpoint in DIFUSCO or T2TCO improves gaps without the modified inference, and using the modified inference with the DIFUSCO checkpoint also improves gaps, showing additive contributions rather than a single self-referential loop. The paper also states that 'only iterating 2-opt on a random Hamiltonian tour produces a tour which optimality gap is at least a few percents', demonstrating that the diffusion model contributes beyond the post-processor. The main methodological weakness is in Section 3.3: the stated objective is a uniform distribution over the R2-equivalence class of the optimal tour, but the implementation samples only two random 2-changes, and the paper does not prove that such samples lie in that equivalence class. This is an attribution/validity concern about whether the retraining gain is due to the claimed equivalence-class objective, not a circularity, because the sampled training targets are not defined in terms of the model's own predictions, and the evaluation is external. There are no load-bearing self-citations: the authors build on DIFUSCO and T2TCO, which are external prior works, and they do not invoke any of their own prior results as a premise for the main claims.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new physical or mathematical entities. Its contributions are algorithmic: an inference-time operator composition and a modified training target distribution. The only hand-chosen quantity is the number of 2-change perturbations (k=2). The key domain assumptions are the validity of the 2-opt equivalence relation and the quality of DIFUSCO's released checkpoints and datasets.

free parameters (1)

k = 2 (number of random 2-change applications) = 2
Section 3.3 chooses two 2-change applications to generate training targets, balancing diversity against computational cost. This is a hand-chosen hyperparameter, not fitted to data, but the method's benefit depends on it.

assumptions (3)

standard math Hamiltonian tours form the relevant solution space and 2-opt is a valid local search on this space
Section 2.1 defines the TSP solution space and the 2-opt operator; this is standard combinatorial optimization background.
domain assumption The DIFUSCO checkpoints and training datasets used for fine-tuning are correctly labeled and reproducible
Section 3.4 initializes from the published DIFUSCO TSP-100 checkpoint and uses the DIFUSCO TSP-500 and TSP-1000 training sets; the paper does not audit these assets.
ad hoc to paper Two random 2-change perturbations of an optimal tour are representative of the 2-opt equivalence class
Section 3.3 replaces the proposed uniform distribution over the equivalence class with exactly two 2-change applications; the paper provides no measurement of how close this sample set is to uniform.

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Cite this review

Pith. "Pith review of IDEQ -- Improving Diffusion Models for the Traveling Salesman Problem (TSP) by Leveraging the Structure of the Solution Space." pith.science (2026). https://pith.science/paper/T2DAYDKX

@misc{pith2026241213858,
  author       = {Pith},
  title        = {Pith review of: IDEQ -- Improving Diffusion Models for the Traveling Salesman Problem (TSP) by Leveraging the Structure of the Solution Space},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T2DAYDKX}},
  note         = {Machine review of arXiv:2412.13858}
}

read the original abstract

We investigate diffusion models to solve the Traveling Salesman Problem. Building on the recent DIFUSCO and T2TCO approaches, we propose IDEQ. IDEQ improves the quality of the solutions by leveraging the constrained structure of the state space of the TSP. Another key component of IDEQ consists in replacing the last stages of DIFUSCO curriculum learning by considering a uniform distribution over the Hamiltonian tours whose orbits by the 2-opt operator converge to the optimal solution as the training objective. Our experiments show that IDEQ improves the state of the art for such neural network based techniques on synthetic instances. More importantly, our experiments show that IDEQ performs very well on the instances of the TSPlib, a reference benchmark in the TSP community: it closely matches the performance of the best heuristics, LKH3, being even able to obtain better solutions than LKH3 on 2 instances of the TSPlib defined on 1577 and 3795 cities. IDEQ obtains 0.3% optimality gap on TSP instances made of 500 cities, and 0.5% on TSP instances with 1000 cities. This sets a new SOTA for neural based methods solving the TSP. Moreover, IDEQ exhibits a lower variance and better scales-up with the number of cities with regards to DIFUSCO and T2TCO.

Figures

Figures reproduced from arXiv: 2412.13858 by the authors.

**Figure 2.** Distribution of optimality gaps measured on 32 rep [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗

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Works this paper leans on

33 extracted references · 29 canonical work pages

[1]

& Berg, R

Austin, J., Johnson, D., Ho, J., Tarlow, D. & Berg, R. Stru ctured Denoising Diﬀusion Models in Discrete State-Spaces. Proc. NeurIPS. pp. 17981-17993 (2021)

work page 2021
[2]

& Dhariwal, P

Nichol, A. & Dhariwal, P. Improved Denoising Diﬀusion Pr obabilistic Mod- els. Proc. ICML. pp. 8162-8171 (2021)

work page 2021
[3]

& Andreoli, J

Drakulic, D., Michel, S., Mai, F., Sors, A. & Andreoli, J. BQ-NCO: Bisim- ulation Quotienting for Eﬃcient Neural Combinatorial Opti mization. Proc. NeurIPS. (2023), https://arxiv.org/abs/2301.03313

arXiv 2023
[4]

An Extension of the Lin-Kernighan-Helsgau n TSP Solver for Constrained Traveling Salesman and Vehicle Routing Problems

Helsgaun, K. An Extension of the Lin-Kernighan-Helsgau n TSP Solver for Constrained Traveling Salesman and Vehicle Routing Problems.. (Technical Report, Roskilde University,2017)

work page 2017
[5]

& Abbeel, P

Ho, J., Jain, A. & Abbeel, P. Denoising Diﬀusion Probabil istic Models. Proc. NeurIPS. pp. 6840-6851 (2020)

work page 2020
[6]

& Salimans, T

Ho, J., Chan, W., Saharia, C., Whang, J., Gao, R., Gritsen ko, A., Kingma, D., Poole, B., Norouzi, M., Fleet, D. & Salimans, T. I magen Video: High Deﬁnition Video Generation with Diﬀusion Model s. (2022), https://arxiv.org/abs/2210.02303

arXiv 2022
[7]

& Wellin g, M

Hoogeboom, E., Nielsen, D., Jaini, P., Forré, P. & Wellin g, M. Argmax Flows and Multinomial Diﬀusion: Learning Categorical Dist ributions. Proc. NeurIPS. pp. 12454-12465 (2021)

work page 2021
[8]

& Welling, M

Hoogeboom, E., Satorras, V., Vignac, C. & Welling, M. Equ ivariant Diﬀu- sion for Molecule Generation in 3D. Proc. ICML. pp. 8867-8887 (2022)

work page 2022

Show all 33 references

[9]

& Carreira, J

Jaegle, A., Gimeno, F., Brock, A., Zisserman, A., Vinyal s, O. & Carreira, J. Perceiver: General Perception with Iterative Attention . Proc. ICML. pp. 4651-4664 (2021)

2021
[10]

& McGeoch, L

Johnson, D. & McGeoch, L. The Traveling Salesman Proble m: A Case Study in Local Optimization. Local Search In Combinatorial Optimisation . pp. 215–310 (1997) 1https://team.inria.fr/scool/ Inria IDEQ: an improved diﬀusion model for the TSP 19

1997
[11]

& Park, J

Kim, M., Park, J. & Park, J. Sym-NCO: Leveraging Symmetr icity for Neu- ral Combinatorial Optimization. Proc. NeurIPS. pp. 1936-1949 (2022)

2022
[12]

& Catanzaro, B

Kong, Z., Ping, W., Huang, J., Zhao, K. & Catanzaro, B. Di ﬀWave: A Versatile Diﬀusion Model for Audio Synthesis. Proc. ICLR. (2021)

2021
[13]

& Welling, M

Kool, W., Hoof, H. & Welling, M. Attention, Learn to Solve Routing Problems!. Proc. ICLR . (2019), https://openreview.net/forum?id=ByxBFsRqYm

2019
[14]

& Gwon, Y

Kwon, Y., Choo, J., Kim, B., Yoon, I., Min, S. & Gwon, Y. PO MO: Pol- icy Optimization with Multiple Optima for Reinforcement Le arning. Proc. NeurIPS. pp. 21188-21198 (2020)

2020
[15]

& Yan, J

Li, Y., Guo, J., Wang, R. & Yan, J. T2T: From Distribution Learning in Training to Gradient Search in Testing for Combinatorial Op timization. Proc. NeurIPS. (2023)

2023
[16]

& Kernighan, B

Lin, S. & Kernighan, B. An eﬀective heuristic algorithm for the traveling salesman problem. Operation Research. 21 pp. 498-516 (1973)

1973
[17]

Liu, J., Wang, Q., Fan, H., Wang, Y., Tang, Y. & Qu, L. Resi dual Denoising Diﬀusion Models. Proc. CVPR. pp. 2773-2783 (2024)

2024
[18]

& Gomes, C

Min, Y., Bai, Y. & Gomes, C. Unsupervised Learning for So lving the Trav- elling Salesman Problem. Proc. NeurIPS. pp. 47264-47278 (2023)

2023
[19]

& Wolf, G

Min, Y., Wenkel, F., Perlmutter, M. & Wolf, G. Can Hybrid Geomet- ric Scattering Networks Help Solve the Maximum Clique Probl em?. Proc. NeurIPS. pp. 22713-22724 (2022)

2022
[20]

& Dhariwal, P

Nichol, A. & Dhariwal, P. Improved Denoising Diﬀusion P robabilistic Mod- els. Proc. ICML. pp. 8162-8171 (2021)

2021
[21]

& Yang, Y

Qiu, R., Sun, Z. & Yang, Y. DIMES: A Diﬀerentiable Meta So lver for Combinatorial Optimization Problems. Proc. NeurIPS . pp. 25531-25546 (2022)

2022
[22]

& Sutskever, I

Ramesh, A., Pavlov, M., Goh, G., Gray, S., Voss, C., Radf ord, A., Chen, M. & Sutskever, I. Zero-Shot Text-to-Image Generation. Proc. ICML. pp. 8821-8831 (2021)

2021
[23]

& Omme r, B

Rombach, R., Blattmann, A., Lorenz, D., Esser, P. & Omme r, B. High- Resolution Image Synthesis with Latent Diﬀusion Models. Proc. CVPR . (2022)

2022
[24]

& Norouzi, M

Saharia, C., Chan, W., Saxena, S., Li, L., Whang, J., Den ton, E., Ghasemipour, S., Ayan, B., Mahdavi, S., Lopes, R., Salimans , T., Ho, J., Fleet, D. & Norouzi, M. Photorealistic Text-to-Image Di ﬀusion Mod- els with Deep Language Understanding. Proc. NeurIPS . pp. 36479-3649...

2022
[25]

& G anguli, S

Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N. & G anguli, S. Deep Un- supervised Learning using Nonequilibrium Thermodynamics . Proc. ICML. pp. 2256-2265 (2015)

2015
[26]

& Ermon, S

Song, J., Meng, C. & Ermon, S. Denoising Diﬀusion Implic it Models. Proc. ICLR. (2020)

2020
[27]

& Yang, Y

Sun, Z. & Yang, Y. DIFUSCO: Graph-based Diﬀusion Solver s for Combinatorial Optimization. Proc. NeurIPS . pp. 3706-3731 (2023), https://openreview.net/forum?id=JV8Ff0lgVV

2023
[28]

& Polosukhin, I

Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jo nes, L., Gomez, A., Kaiser, L. & Polosukhin, I. Attention Is All You Need. Proc. NeurIPS. (2017)

2017
[29]

& Frossard, P

Vignac, C., Krawczuk, I., Siraudin, A., Wang, B., Cevhe r, V. & Frossard, P. DiGress: Discrete Denoising diﬀusion for graph generati on. Proc. ICLR. (2023)

2023
[30]

& Tang, J

Xu, M., Yu, L., Song, Y., Shi, C., Ermon, S. & Tang, J. GeoD iﬀ: a Geomet- ric Diﬀusion Model for Molecular Conformation Generation. Proc. ICLR. (2022)

2022
[31]

& Zhu, C

Yu, K., Zhao, H., Huang, Y., Yi, R., Xu, K. & Zhu, C. DISCO: Eﬃ- cient Diﬀusion Solver for Large-Scale Combinatorial Optim ization Prob- lems. (2024), https://arxiv.org/abs/2406.19705

2024 arXiv
[32]

& Zhang, Q

Zhou, C., Lin, X., Wang, Z., Tong, X., Yuan, M. & Zhang, Q. Instance- Conditioned Adaptation for Large-scale Generalization of Neural Combi- natorial Optimization. (2024), arXiv:2405.01906

2024 arXiv
[33]

& Duan, Z

Zhu, G., Wen, Y., Carbonneau, M. & Duan, Z. EDMSound: Spe ctrogram Based Diﬀusion Models for Eﬃcient and High-Quality Audio Sy nthesis. (2023), NeurIPS workshop: machine learning for audio Inria IDEQ: an improved diﬀusion model for the TSP 21 A Detailed results on the instance...

2023

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

& Berg, R

Austin, J., Johnson, D., Ho, J., Tarlow, D. & Berg, R. Stru ctured Denoising Diﬀusion Models in Discrete State-Spaces. Proc. NeurIPS. pp. 17981-17993 (2021)

work page 2021

[2] [2]

& Dhariwal, P

Nichol, A. & Dhariwal, P. Improved Denoising Diﬀusion Pr obabilistic Mod- els. Proc. ICML. pp. 8162-8171 (2021)

work page 2021

[3] [3]

& Andreoli, J

Drakulic, D., Michel, S., Mai, F., Sors, A. & Andreoli, J. BQ-NCO: Bisim- ulation Quotienting for Eﬃcient Neural Combinatorial Opti mization. Proc. NeurIPS. (2023), https://arxiv.org/abs/2301.03313

arXiv 2023

[4] [4]

An Extension of the Lin-Kernighan-Helsgau n TSP Solver for Constrained Traveling Salesman and Vehicle Routing Problems

Helsgaun, K. An Extension of the Lin-Kernighan-Helsgau n TSP Solver for Constrained Traveling Salesman and Vehicle Routing Problems.. (Technical Report, Roskilde University,2017)

work page 2017

[5] [5]

& Abbeel, P

Ho, J., Jain, A. & Abbeel, P. Denoising Diﬀusion Probabil istic Models. Proc. NeurIPS. pp. 6840-6851 (2020)

work page 2020

[6] [6]

& Salimans, T

Ho, J., Chan, W., Saharia, C., Whang, J., Gao, R., Gritsen ko, A., Kingma, D., Poole, B., Norouzi, M., Fleet, D. & Salimans, T. I magen Video: High Deﬁnition Video Generation with Diﬀusion Model s. (2022), https://arxiv.org/abs/2210.02303

arXiv 2022

[7] [7]

& Wellin g, M

Hoogeboom, E., Nielsen, D., Jaini, P., Forré, P. & Wellin g, M. Argmax Flows and Multinomial Diﬀusion: Learning Categorical Dist ributions. Proc. NeurIPS. pp. 12454-12465 (2021)

work page 2021

[8] [8]

& Welling, M

Hoogeboom, E., Satorras, V., Vignac, C. & Welling, M. Equ ivariant Diﬀu- sion for Molecule Generation in 3D. Proc. ICML. pp. 8867-8887 (2022)

work page 2022