Pith. sign in

REVIEW 4 major objections 6 minor 42 references

Constraint-Aware Diffusion Guidance for Robotics: Real-Time Obstacle Avoidance for Autonomous Racing

T0 review · 4 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Adding the gradient of a barrier function to the denoising score lets a diffusion-based planner dodge obstacles in real time, replanning at 2.5 Hz on a real miniature race car without retraining on obstacle data.

desk verdict Real hardware demo, but the proposed barrier guidance as written has no obstacle gradient—needs a fix before the central claim is credible. read the letter →

arxiv 2505.13131 v1 pith:XP3DHG33 submitted 2025-05-19 cs.RO cs.SYeess.SY

Hao Ma , Sabrina Bodmer , Andrea Carron , Melanie Zeilinger , Michael Muehlebach This is my paper · ORCID
classification cs.ROcs.SYeess.SY
keywords constraint-awarediffusionguidancebarrierfunctionscore-basedgenerativemodelsreal-timeobstacleavoidanceautonomousracingwarm-startinferencesafetrajectorygenerationFrenetframeplanning
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

CoDiG is a recipe for making a diffusion-based trajectory planner respect safety constraints it never saw during training: during denoising, the learned score is augmented with the gradient of a barrier function that penalizes trajectories that leave the obstacle-free region. The paper claims that this one additive term turns a data-efficient diffusion planner, trained on a few thousand offline time-optimal demonstrations, into an obstacle-avoidance system that replans safely at 2.5 Hz. On a real miniature race car with static and moving obstacles, the system reports a 100% success rate over 75 laps, while the tracking controller needs no obstacle information of its own. The reason to care is that constraint handling moves from training time to inference time: the same pretrained generative model can be steered around novel, moving obstacles without retraining, auxiliary classifiers, or projection steps.

What carries the argument

The load-bearing object is the modified reverse SDE in Eq. (6), in which the unconstrained score $s_\theta(x_t,t)$ is replaced by $s_\theta(x_t,t) - \gamma_t \nabla_x V(x_t;\mathcal{C})$, together with the identity behind it, $\nabla_x \log p_t(x_t|\mathcal{C}) = \nabla_x \log p_t(x_t) - \gamma_t \nabla_x V(x_t;\mathcal{C})$. This identity turns constraint satisfaction into an additive gradient term evaluated during denoising, so one pretrained, constraint-blind score network can handle arbitrary time-varying obstacle sets at inference. The barrier $V$ is then doubly functional: an indicator term over the obstacle-free Frenet region enforces collision avoidance, while a quadratic penalty toward the offline nominal trajectory supplies the global-curvature information missing from the local-coordinate training representation, and with it dynamic feasibility and near time-optimality. Two stabilizers carry the real-time claim: a sigmoid-scheduled $\gamma_t$ that stays near zero while samples are still close to noise, so guidance acts only once trajectory structure has formed, and the warm start, which re-initializes the sampler from the previous reference with added noise, cutting the denoising budget from 1000 to 50 steps at an acceptable cost in trajectory coarseness and conservatism.

What would settle it

Fix a static obstacle layout and run the same trained score network under three samplers: (a) the guided reverse SDE in Eq. (6) exactly as written; (b) a literal implementation of the tilt, which draws clean trajectories from the unconstrained model and reweights them by the exponential of minus the barrier value times the schedule coefficient; and (c) rejection sampling that keeps only trajectories whose final points lie inside the feasible set. If (a) and (b) differ in collision frequency or in the distribution of generated trajectories under the identical schedule of guidance weights, then the reverse SDE is not sampling the claimed conditional distribution, and the reported 100% avoidance success must be credited to the warm-start replanning loop rather than to the barrier guidance itself.

Watch

Extended reading notes

Core claim

The paper's central claim is that conditioning the denoising process on a feasible set $\mathcal{C}$ is, for sampling purposes, equivalent to replacing the learned score with $s_\theta(x_t,t) - \gamma_t \nabla_x V(x_t;\mathcal{C})$, where $V$ is a barrier potential. This rests on the exponential-tilt identity $p_t(x_t|\mathcal{C}) \propto p_t(x_t)\exp(-\gamma_t V(x_t;\mathcal{C}))$, whose log-gradient cancels the partition function, so the constraint enters the reverse SDE in Eq. (6) as an additive, time-varying gradient term and never appears in a training objective. In the racing case study, the barrier combines an indicator that the trajectory points stay inside the obstacle-free Frenet corridor with a quadratic pull toward the offline nominal time-optimal trajectory, the latter restoring track-curvature information the authors deliberately discard when transforming data into local coordinates. With a warm start that re-initializes sampling from the previous output plus small noise, the 1000-step denoising budget drops to roughly 50 steps and the replanning rate reaches 2.5 Hz; the real-car experiments report 100% avoidance success over 75 laps across ten obstacle configurations, and the generated paths remain close to offline time-optimal solutions.

Load-bearing premise

The whole mechanism assumes that conditioning the sampler on the obstacle-free region is exactly equivalent to multiplying the sampling density by a barrier penalty evaluated on noisy intermediate samples, even though the penalty is defined on clean final trajectories and jumps discontinuously at the obstacle boundary; if that equivalence, or the claim that the noise-modified reverse SDE in Eq. (6) samples from it, fails during denoising, the guided sampler is a heuristic that only resembles a constrained generator.

Editorial extensions

If this is right

  • Constraint-compliant training data is no longer required: the same network trained on time-optimal demonstrations avoids unseen static and moving obstacles purely through the inference-time barrier gradient.
  • Replanning rate rises from 0.25 Hz with 1000 denoising steps from pure noise to 2.5 Hz with 50 warm-started steps, entering the real-time budget of the racing platform.
  • The tracking controller operates without obstacle information, and the close agreement between CoDiG references and TMPC predictions indicates the guidance preserves dynamic feasibility well enough for safe closed-loop execution.
  • Because only the potential $V$ is task-specific, the same guidance mechanism transfers to other robotics tasks by redefining the barrier and its gradient.
  • Near time-optimality survives constraint handling: deviations from the offline optimum appear only as extra clearance near obstacles and larger cornering radii, per the offline comparisons.

Reading between the lines

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

  • The exponential-tilt construction is the same mechanism that powers classifier guidance in image generation; read that way, CoDiG's contribution is transferring that scheme from pixel-space classifiers to physically meaningful, time-varying barrier potentials and demonstrating it live on hardware.
  • Because the collision penalty in the barrier is an indicator function, the guidance gradient is formally a subgradient; the experiments suggest this is benign in practice, but replacing it with a smoothed penalty would make the guidance a true gradient flow and should remove any discretization artifacts in the Euler-Maruyama update.
  • The reported 100% success rate bundles the barrier guidance with the warm-start replanning loop and the tracking controller; ablating each component, with guidance off, warm start off, or a safety-filter MPC in place of the diffusion planner, would reveal which one actually carries the safety guarantee.
  • The warm-start conservatism documented in the appendix implies a speed-versus-aggressiveness trade-off: in a scenario demanding a late, sharp escape, such as overtaking into a narrow gap, the pull toward the previous trajectory could delay the maneuver, a regime the static-plus-dynamic obstacle setup does not stress.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper proposes Constraint-Aware Diffusion Guidance (CoDiG), a method that integrates a barrier function into the reverse diffusion process by adding the gradient of a penalty potential to the score function. The method is evaluated on a miniature autonomous racing platform, using a warm-start strategy to accelerate sampling and a tracking MPC to follow the generated trajectories. The authors report a 2.5 Hz planning frequency and a 100% success rate in obstacle avoidance over five trials of 15 laps each.

Significance. The paper addresses an important practical problem: enforcing safety constraints during diffusion-based trajectory generation without retraining. The real-world experimental platform and the demonstration of real-time planning are valuable strengths, as is the detailed description of the experimental setup and the barrier-function design for a concrete robotic task. However, the theoretical grounding of the constraint guidance is unsound as presented: the proposed barrier function's first term is piecewise constant and provides no gradient information, the modified reverse SDE is not shown to sample the claimed tilted distribution, and the experiments lack an ablation that isolates the guidance's effect. If these issues are addressed with a smooth surrogate, a rigorous derivation, and proper ablations, the work could be a meaningful contribution to inference-time constraint handling in diffusion models.

major comments (4)
  1. [Sec. 4.1, Eq. (7)] The first part of the barrier function V is α Σ_k 1{ŷ_k ∉ C_k}, which is piecewise constant as a function of the trajectory. Its gradient with respect to x_t is zero almost everywhere and undefined on the boundary of C_k. Consequently, ∇_x V in Eq. (5) contains no obstacle-avoidance signal; the only effective guidance comes from the quadratic nominal-tracking terms. This contradicts the central claim that 'the barrier function contributes no directional information about obstacles' and that the method 'guides sampling toward safe, obstacle-free regions.' The equations can be simulated, but the stated mechanism is not what Eq. (7) implements.
  2. [Sec. 3.2, definition of p_t(x_t|C)] The paper defines p_t(x_t|C) ∝ p_t(x_t) exp(-γ_t V(x_t;C)) and calls this 'the constrained distribution.' This is an exponential tilt, not the conditional distribution p_t(x_t | C) = p_t(x_t) 1{x_t ∈ C} / P(C). Moreover, V in Eq. (7) is evaluated on clean trajectory components (ŷ, φ̂), while the reverse SDE in Eq. (6) applies ∇_x V to the noisy state x_t at intermediate diffusion times. No argument is provided that penalizing V on noisy samples correctly biases the final clean sample toward C. The paper should either justify this tilt as a valid approximation of conditioning or present it explicitly as a heuristic.
  3. [Sec. 3.2, Eq. (6)] The modified reverse SDE introduces η as a scaling of both the drift correction and the noise coefficient. Standard reverse-time SDE theory fixes the noise coefficient at g(t) to recover the forward process's marginal distributions; changing it to η√(2β(t)) while scaling the drift by (1+η) alters the invariant distribution. The paper cites [30] but does not show that the modified process samples from the claimed tilted distribution p_t(x_t|C). As written, Eq. (6) is an ad hoc heuristic, and the theoretical guarantee that 'guiding diffusion sampling toward constraint-satisfying outputs' works is not established.
  4. [Sec. 5.2 and Fig. 1] The real-world experiments report a 100% success rate over 75 laps, but they do not include an ablation that removes the guidance term (e.g., setting α = 0) or a comparison against the unguided diffusion model on the same obstacle configurations. Since the indicator gradient in Eq. (7) is zero almost everywhere, the experiments as reported cannot verify that the barrier function is the cause of obstacle avoidance; the success may be due to the trained U-Net, the warm-start initialization, or the tracking MPC. A proper ablation is necessary to support the central claim that the proposed constraint-aware guidance is responsible for the reported performance.
minor comments (6)
  1. [Sec. 4.1] The term 'barrier function' is misleading, since V does not diverge at the boundary of C but instead is an indicator plus a quadratic penalty; consider renaming it 'constraint penalty' or 'guidance potential.'
  2. [Eq. (7)] The symbols ŷ and φ̂ are used without explicitly relating them to the diffusion state x_t; clarify whether V is evaluated on the full trajectory x_0 or on the noisy sample x_t at each diffusion time step.
  3. [Appendix B, Eq. (8)] The Euler-Maruyama update uses x_k both for the noisy sample and for the mean estimate ̅x_k; the notation is confusing and should be made consistent.
  4. [Fig. 5] The training loss curves in Fig. 5 lack clear labels for the different configurations beyond the legend entries; consider adding explicit plot titles and reporting validation loss in addition to training loss.
  5. [Sec. 5.2] The description of the experimental protocol ('five experimental trials, each consisting of 15 racing laps, across ten different obstacle configurations') is ambiguous: it is unclear how many laps were run per configuration and whether the dynamic obstacles moved on a fixed schedule or unpredictably; please specify the protocol more precisely.
  6. [References] Reference [30] is cited for the η modification, but the cited work does not appear to introduce this form of noise scaling; please provide a direct derivation or a more appropriate citation.

Circularity Check

1 steps flagged · score 6.0 of 10

The reported near time-optimality is a restatement of the quadratic nominal-tracking term in the barrier function, not an independent prediction; no load-bearing self-citation was found.

  1. self definitional [Eq. (7), Sec. 4.1; Sec. 5.2 near time-optimality claim; Appendix E]
    "V(ŷ, φ̂; C) = Σ_{k=0}^{N-1} [α 1{ŷ_k ∉ C_k} + (ε/2)|ŷ_k − ŷ_nominal,k|² + (ε/2)|φ̂_k − φ̂_nominal,k|²] ... The second part ... promotes near time-optimality without requiring global geometric knowledge of the track ... 'we demonstrate the near time-optimality of the trajectories generated by CoDiG by comparing them with trajectories obtained by solving an offline time-optimal control problem.'"

    Equation (7) explicitly penalizes squared deviation from ŷ_nominal and φ̂_nominal, which the paper defines as the offline time-optimal solution. Since Eq. (5) and the Euler-Maruyama update in Eq. (8) inject the term −γ_t ∇_x V into the score, the generated trajectories are directly pulled toward that same nominal time-optimal trajectory. Appendix E then reports a 'high degree of similarity' to the offline time-optimal path, and Sec. 5.2 claims 'near time-optimality.' The match is therefore a restatement of the objective encoded in V, not an independent prediction: any sample that follows the guidance will be close to the nominal by construction, independent of the learned data distribution.

full rationale

The core score modification in Eq. (5) is an explicit exponential-tilt ansatz: the constrained distribution is defined as p_t(x_t|C) = p_t(x_t)e^{-γ_t V}/Z_t, and the score identity ∇log p_t(x_t|C) = ∇log p_t(x_t) - γ_t∇V is a mathematical consequence of that definition. This is a modeling choice, not a hidden circular derivation. No load-bearing self-citation was found: Ref. [25] includes a co-author but is used only as a related-work remark about autoregressive alternatives, and the other citations are not author-overlapping or are not load-bearing. The concrete circular step is the evaluation of near time-optimality: the second term of Eq. (7) is literally a quadratic penalty pulling samples toward the nominal time-optimal trajectory, and Appendix E compares against exactly that nominal trajectory. Separately, there is a non-circular correctness risk: the first term of V is α 1{ŷ_k ∉ C_k}, whose classical gradient is zero almost everywhere, so as written the guidance term in Eq. (8) contains no obstacle-avoidance signal from that term; this makes the stated safety mechanism unverifiable but is an inconsistency rather than a circularity. Because one reported property (near time-optimality) reduces by construction while the obstacle-avoidance success rate is an empirical result, the overall circularity is partial.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The safety and optimality properties of CoDiG depend on a hand-designed barrier function with tuned weights, a heuristic SDE modification, and a precomputed nominal trajectory. The diffusion model contributes the learned data distribution, but the headline behaviors, collision avoidance and near time-optimality, are substantially shaped by these free parameters.

free parameters (7)
  • eta = 0.1
    Scales the noise term in the reverse SDE; introduced for stability and convergence without derivation.
  • alpha = 0.4
    Weight of the obstacle-violation indicator in the barrier function, hand-tuned.
  • epsilon = 16.0
    Weight of the attraction to the nominal time-optimal trajectory; strongly shapes generated trajectories toward the precomputed racing line.
  • gamma(t) schedule (h1, h2, h3) = 1.0, 50.0, 0.7
    Time-varying guidance strength that ramps up during denoising; values chosen by hand.
  • time discretization exponent p = 2.2
    Controls the non-uniform diffusion time grid in the Euler-Maruyama scheme.
  • beta(t) schedule (r1, r0) = r1=100.0, r0=30.0
    Noise schedule parameters selected after training experiments; used in the SDE and denoising updates.
  • nominal trajectory (y_nominal, phi_nominal) = offline time-optimal path without obstacles
    Serves as a prior in the barrier function; its choice largely determines the 'near time-optimality' result.
assumptions (5)
  • standard math Reverse-time SDE theory (Song et al. 2021; Anderson 1982) that the score-based reverse process samples the data distribution.
    The paper builds on the standard score-based generative modeling framework and uses it as the starting point for the constrained sampler.
  • ad hoc to paper The constrained conditional distribution can be written as p_t(x_t|C) proportional to p_t(x_t) exp(-gamma_t V(x_t;C)) / Z_t.
    This exponential tilt is asserted in Sec. 3.2; it is not equivalent in general to conditioning on the final trajectory being in C, but all subsequent equations rely on it.
  • ad hoc to paper The reverse SDE with modified noise coefficient eta in Eq. (6) still produces samples from the tilted distribution p_t(x_t|C).
    No proof is given that adding eta preserves the target distribution; this is a heuristic acceleration.
  • ad hoc to paper The barrier function V in Eq. (7) is differentiable with respect to x_t and can be evaluated on noisy samples.
    V contains the discontinuous indicator 1{y_k not in C_k}, so the gradient used in the guidance term is not well-defined as written.
  • domain assumption The synthetic training set, produced by time-optimal control with redundant obstacle augmentation, covers the test scenarios well enough for generalization.
    The generalization claims rest on this dataset; the paper uses 100 base optimal trajectories expanded to 10,000 and does not analyze coverage of the obstacle space.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Constraint-Aware Diffusion Guidance for Robotics: Real-Time Obstacle Avoidance for Autonomous Racing." pith.science (2026). https://pith.science/paper/XP3DHG33

@misc{pith2026250513131,
  author       = {Pith},
  title        = {Pith review of: Constraint-Aware Diffusion Guidance for Robotics: Real-Time Obstacle Avoidance for Autonomous Racing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XP3DHG33}},
  note         = {Machine review of arXiv:2505.13131}
}
read the original abstract

Diffusion models hold great potential in robotics due to their ability to capture complex, high-dimensional data distributions. However, their lack of constraint-awareness limits their deployment in safety-critical applications. We propose Constraint-Aware Diffusion Guidance (CoDiG), a data-efficient and general-purpose framework that integrates barrier functions into the denoising process, guiding diffusion sampling toward constraint-satisfying outputs. CoDiG enables constraint satisfaction even with limited training data and generalizes across tasks. We evaluate our framework in the challenging setting of miniature autonomous racing, where real-time obstacle avoidance is essential. Real-world experiments show that CoDiG generates safe outputs efficiently under dynamic conditions, highlighting its potential for broader robotic applications. A demonstration video is available at https://youtu.be/KNYsTdtdxOU.

Figures

Figures reproduced from arXiv: 2505.13131 by the authors.

Figure 1
Figure 1. Intermediate denoising results during sampling at three representative time steps [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Real-world demonstration of real-time obstacle avoidance using CoDiG. Red lines repre [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. (a) A time-optimal trajectory (red line) computed for a given obstacle configuration (gray [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Architecture of the proposed time-conditioned score-based generative model. The U [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: Training performance of the diffusion model under different input configurations and noise [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: Comparison of reference trajectories generated with and without the warm start technique [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: Comparison between trajectories generated in real time by CoDiG (red) and offline [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: Experimental platform used to evaluate the performance of the CoDiG framework for real [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: Flowchart of the proposed CoDiG framework for real-time obstacle avoidance in au [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 25 canonical work pages

  1. [30]

    Song and S

    Y . Song and S. Ermon. Improved Techniques for Training Score-Based Generative Models. In Advances in Neural Information Processing Systems, pages 12438–12448, 2020

    work page 2020

  2. [1]

    Sohl-Dickstein, E

    J. Sohl-Dickstein, E. Weiss, N. Maheswaranathan, and S. Ganguli. Deep Unsupervised Learn- ing using Nonequilibrium Thermodynamics. In International Conference on Machine Learn- ing, pages 2256–2265, 2015

    work page 2015

  3. [2]

    J. Ho, A. Jain, and P. Abbeel. Denoising Diffusion Probabilistic Models. InAdvances in Neural Information Processing Systems, pages 6840–6851, 2020

    work page 2020

  4. [3]

    J. Ho, C. Saharia, W. Chan, D. J. Fleet, M. Norouzi, and T. Salimans. Cascaded Diffusion Models for High Fidelity Image Generation. Journal of Machine Learning Research, 23(47): 1–33, 2022

    work page 2022

  5. [4]

    Batzolis, J

    G. Batzolis, J. Stanczuk, C.-B. Sch ¨onlieb, and C. Etmann. Conditional Image Generation with Score-Based Diffusion Models. arXiv:2111.13606, pages 1–19, 2021

    arXiv 2021

  6. [5]

    Jeong, H

    M. Jeong, H. Kim, S. J. Cheon, B. J. Choi, and N. S. Kim. Diff-TTS: A Denoising Diffusion Model for Text-to-Speech. arXiv:2104.01409, pages 1–5, 2021

    arXiv 2021

  7. [6]

    J. Ho, T. Salimans, A. Gritsenko, W. Chan, M. Norouzi, and D. J. Fleet. Video Diffusion Models. In Advances in Neural Information Processing Systems, pages 8633–8646, 2022

    work page 2022

  8. [7]

    R. Wolf, Y . Shi, S. Liu, and R. Rayyes. Diffusion Models for Robotic Manipulation: A Survey. arXiv:2504.08438, pages 1–28, 2025

    arXiv 2025

Show all 42 references
  1. [8]

    C. Chi, Z. Xu, S. Feng, E. Cousineau, Y . Du, B. Burchfiel, R. Tedrake, and S. Song. Diffusion policy: Visuomotor policy learning via action diffusion. The International Journal of Robotics Research, 0(0):1–21, 2024

    2024

  2. [9]

    Urain, N

    J. Urain, N. Funk, J. Peters, and G. Chalvatzaki. SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion. In International Conference on Robotics and Automation, pages 5923–5930, 2023

    2023

  3. [10]

    Kondo, A

    K. Kondo, A. Tagliabue, X. Cai, C. Tewari, O. Garcia, M. Espitia-Alvarez, and J. P. How. CGD: Constraint-Guided Diffusion Policies for UA V Trajectory Planning.arXiv:2405.01758, pages 1–8, 2024

    2024 arXiv

  4. [11]

    N. D. Palo, L. Hasenclever, J. Humplik, and A. Byravan. Diffusion Augmented Agents: A Framework for Efficient Exploration and Transfer Learning. InConference on Lifelong Learn- ing Agents, pages 268–284, 2025

    2025

  5. [12]

    K. M. Lee, S. Ye, Q. Xiao, Z. Wu, Z. Zaidi, D. B. D’Ambrosio, P. R. Sanketi, and M. Gom- bolay. Learning Diverse Robot Striking Motions with Diffusion Models and Kinematically Constrained Gradient Guidance. arXiv:2409.15528, pages 1–8, 2025

    2025 arXiv

  6. [13]

    Liang, Y

    Z. Liang, Y . Mu, M. Ding, F. Ni, M. Tomizuka, and P. Luo. AdaptDiffuser: Diffusion Models as Adaptive Self-evolving Planners. In International Conference on Machine Learning, pages 20725–20745, 2023

    2023

  7. [14]

    Bastek, W

    J.-H. Bastek, W. Sun, and D. M. Kochmann. Physics-Informed Diffusion Models. arXiv:2403.14404, pages 1–26, 2025. 9

    2025 arXiv

  8. [15]

    Giannone, A

    G. Giannone, A. Srivastava, O. Winther, and F. Ahmed. Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation. InAdvances in Neural Information Processing Systems, pages 51830–51861, 2023

    2023

  9. [16]

    Power, R

    T. Power, R. Soltani-Zarrin, S. Iba, and D. Berenson. Sampling Constrained Trajectories Using Composable Diffusion Models. InInternational Conference on Intelligent Robots and Systems, pages 1–5, 2023

    2023

  10. [17]

    Carvalho, A

    J. Carvalho, A. T. Le, M. Baierl, D. Koert, and J. Peters. Motion Planning Diffusion: Learn- ing and Planning of Robot Motions with Diffusion Models. In International Conference on Intelligent Robots and Systems, pages 1916–1923, 2023

    1916

  11. [18]

    J. K. Christopher, S. Baek, and F. Fioretto. Constrained Synthesis with Projected Diffusion Models. arXiv:2402.03559, pages 1–20, 2024

    2024 arXiv

  12. [19]

    Xiao, T.-H

    W. Xiao, T.-H. Wang, C. Gan, and D. Rus. SafeDiffuser: Safe Planning with Diffusion Proba- bilistic Models. arXiv:2306.00148, pages 1–19, 2023

    2023 arXiv

  13. [20]

    R ¨omer, A

    R. R ¨omer, A. von Rohr, and A. P. Schoellig. Diffusion Predictive Control with Constraints. arXiv:2412.09342, pages 1–14, 2024

    2024 arXiv

  14. [21]

    W. Yu, J. Peng, H. Yang, J. Zhang, Y . Duan, J. Ji, and Y . Zhang. LDP: A Local Diffusion Planner for Efficient Robot Navigation and Collision Avoidance. In International Conference on Intelligent Robots and Systems, pages 5466–5472, 2024

    2024

  15. [22]

    A. Ajay, Y . Du, A. Gupta, J. Tenenbaum, T. Jaakkola, and P. Agrawal. Is Conditional Genera- tive Modeling All You Need for Decision-Making? arXiv:2211.15657, pages 1–24, 2023

    2023 arXiv

  16. [23]

    Z. Gong, A. Kumar, and P. Varakantham. Offline Safe Reinforcement Learning Using Trajec- tory Classification. In Conference on Artificial Intelligence, pages 16880–16887, 2025

    2025

  17. [24]

    Botteghi, F

    N. Botteghi, F. Califano, M. Poel, and C. Brune. Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Models. arXiv:2306.15512, pages 1–18, 2023

    2023 arXiv

  18. [25]

    Sheebaelhamd, M

    Z. Sheebaelhamd, M. Tschannen, M. Muehlebach, and C. Vernade. Quantization-Free Autore- gressive Action Transformer. arXiv:2503.14259, pages 1–15, 2025

    2025

  19. [26]

    Y . Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole. Score-Based Generative Modeling through Stochastic Differential Equations. In International Conference on Machine Learning, pages 10362–10383, 2021

    2021

  20. [27]

    Øksendal

    B. Øksendal. Stochastic Differential Equations. Springer Berlin Heidelberg, 1995

    1995

  21. [28]

    B. D. Anderson. Reverse-Time Diffusion Equation Models. Stochastic Processes and their Applications, 12(3):313–326, 1982

    1982

  22. [29]

    Ho and T

    J. Ho and T. Salimans. Classifier-Free Diffusion Guidance. arXiv:2207.12598, pages 1–14, 2022

    2022 arXiv

  23. [31]

    Bodmer, L

    S. Bodmer, L. V ogel, S. Muntwiler, A. Hansson, T. Bodewig, J. Wahlen, M. N. Zeilinger, and A. Carron. Optimization-Based System Identification and Moving Horizon Estimation Using Low-Cost Sensors for a Miniature Car-Like Robot. arXiv:2404.08362, pages 1–11, 2024

    2024 arXiv

  24. [32]

    Carron, S

    A. Carron, S. Bodmer, L. V ogel, R. Zurbr¨ugg, D. Helm, R. Rickenbach, S. Muntwiler, J. Sieber, and M. N. Zeilinger. Chronos and CRS: Design of a miniature car-like robot and a software framework for single and multi-agent robotics and control. In International Conference on R...

    2023

  25. [33]

    J. Song, C. Meng, and S. Ermon. Denoising Diffusion Implicit Models. arXiv:2010.02502, pages 1–22, 2022

    2010 arXiv

  26. [34]

    Zhang and Y

    Q. Zhang and Y . Chen. Fast Sampling of Diffusion Models with Exponential Integrator. arXiv:2204.13902, pages 1–33, 2023

    2023 arXiv

  27. [35]

    Morari and J

    M. Morari and J. H. Lee. Model predictive control: past, present and future. Computers & Chemical Engineering, 23(4-5):667–682, 1999

    1999

  28. [36]

    Limon, I

    D. Limon, I. Alvarado Aldea, T. Alamo, and E. F. Camacho. MPC for tracking piecewise constant references for constrained linear systems. Automatica, 44(9):2382–2387, 2008

    2008

  29. [37]

    Soloperto, J

    R. Soloperto, J. K ¨ohler, and F. Allg ¨ower. A Nonlinear MPC Scheme for Output Tracking Without Terminal Ingredients. Transactions on Automatic Control, 68(4):2368–2375, 2023

    2023

  30. [38]

    T. Sauer. Numerical Solution of Stochastic Differential Equations in Finance. In Handbook of Computational Finance, pages 529–550. Springer, 2012

    2012

  31. [39]

    Verschueren, M

    R. Verschueren, M. Zanon, R. Quirynen, and M. Diehl. Time-optimal Race Car Driving using an Online Exact Hessian based Nonlinear MPC Algorithm. In European Control Conference, pages 141–147, 2016

    2016

  32. [40]

    H. C. Crenshaw and L. Edelstein-Keshet. Orientation by Helical Motion—II. Changing the Direction of the Axis of Motion. Bulletin of Mathematical Biology, 55(1):213–230, 1993

    1993

  33. [41]

    Rombach, A

    R. Rombach, A. Blattmann, D. Lorenz, P. Esser, and B. Ommer. High-Resolution Image Synthesis with Latent Diffusion Models. arXiv:2112.10752, pages 1–45, 2022

    2022 arXiv

  34. [42]

    Hensman, N

    J. Hensman, N. Durrande, and A. Solin. Variational Fourier Features for Gaussian Processes. Journal of Machine Learning Research, 18(151):1–52, 2018. 11 A Hyperparameters During inference, the hyperparameters are set as follows: η = 0.1, α = 0.4, ϵ = 16.0. In particular, the t...

    2018

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.