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REVIEW 3 major objections 4 minor 1 cited by

STFlow: Data-Coupled Flow Matching for Geometric Trajectory Simulation

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read STFlow starts trajectory simulation from a random-walk prior fitted to observed frames and reports the lowest prediction errors among compared baselines with only five integration steps.

desk verdict A genuinely useful informed-prior idea with strong ablations, but the paper's 'lowest prediction errors' claim is contradicted by its own tables; with tempered claims it deserves peer review. read the letter →

arxiv 2505.18647 v3 pith:ZZ2GS6XZ submitted 2025-05-24 cs.LG cs.AI

Kiet Bennema ten Brinke , Koen Minartz , Vlado Menkovski This is my paper
classification cs.LGcs.AI
keywords flowmatchingtrajectorypredictiondata-dependentcouplingrandom-walkpriorequivariantgraphneuralnetworksgenerativemodelingN-bodysystemsmoleculardynamics
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

This paper argues that conditional trajectory simulation by flow matching should start from a prior built from the observed frames, not from Gaussian noise. It introduces STFlow, which constructs a per-trajectory random-walk prior whose drift and velocity variance are estimated from the conditioning frames, and learns a vector field that straightens the probability path from that prior to the data. On N-body physics, molecular dynamics (MD17), and basketball player trajectories, STFlow reports the lowest prediction errors among the compared baselines while using only five Euler integration steps. The claim matters because it suggests that embedding conditioning information into the prior, rather than only into the network input, is a cheap and transferable way to make generative trajectory models both more accurate and cheaper to run.

What carries the argument

The carrying device is the data-dependent random-walk prior of Eq. (2): a stochastic process $\zeta_t = \zeta_{t-1} + \mu + \sigma_o \odot z_t$ whose drift $\mu$ and velocity scale $\sigma_o$ are computed from the observed conditioning frames, while the observed coordinates themselves are kept intact in $x_0$. This makes the source distribution $p_0$ close to the target $p_1$, so the optimal transport vector field $u = x_1 - x_0$ is small and nearly straight, and five Euler steps suffice. The architecture then only needs to learn the residual correction: spatial message-passing layers handle interactions between particles, and a temporal convolution (UNet) layer handles multi-scale time correlations while preserving permutation and time-shift symmetries.

What would settle it

Construct a two-phase system, for example particles moving ballistically for the first $c$ frames and then suddenly subjected to a constant external force or a reflecting wall, and compare STFlow's five-step error against its own Gaussian-prior variant and against a high-NFE version; if errors degrade sharply and increasing the number of steps does not recover them, the claim that the random-walk prior reduces transport cost enough for five-step inference fails. More directly, measuring the mean $\|x_1 - x_0\|$ transport cost on such a dataset and finding little or no reduction relative to a Gaussian prior would refute the mechanism.

Watch

Extended reading notes

Core claim

The central claim is that a data-dependent random-walk prior makes flow matching learn a straighter, shorter path from prior to data, so that very few integration steps suffice for accurate trajectory simulation. STFlow keeps the observed frames intact and replaces the unobserved future with a random walk $\zeta_t = \zeta_{t-1} + \mu + \sigma_o \odot z_t$, where $\mu$ and $\sigma_o$ are the drift and velocity variance estimated from the observed frames. Training still uses the standard conditional flow-matching loss $\mathcal{L}_{\mathrm{CFM}} = \mathbb{E} \| v_\theta(x_\tau, h, E, \tau) - (x_1 - x_0) \|^2$, but because $x_0$ already reflects the true dynamics, the target vector field $u = x_1 - x_0$ has small magnitude and is nearly straight. Across the three benchmarks the paper reports the lowest ADE and FDE among the compared methods, with a mean decrease in prediction error ranging from about 16.7% to 56.9% while using only five function evaluations. The reported density comparisons show the learned mapping corrects the unimodal prior into the multimodal velocity and acceleration distributions of the data.

Load-bearing premise

The future trajectory is well approximated by a random walk whose drift and velocity variance are estimated from the observed frames; if the dynamics change character after the conditioning window, the prior is misaligned and the model must learn large corrections from only five Euler steps.

Editorial extensions

If this is right

  • With an aligned prior, flow matching reaches near state-of-the-art trajectory accuracy in about five function evaluations instead of hundreds, making probabilistic simulation of long horizons practical.
  • The same random-walk prior works on charged-particle, spring, gravity, molecular-dynamics, and basketball-tracking data without domain-specific features, so the recipe is transferable across trajectory domains.
  • Replacing the informed prior with a Gaussian or an uncoupled random walk increases prediction error by roughly 85% and 74%, respectively, showing the coupling, not the architecture alone, carries most of the benefit.
  • Because the spatio-temporal architecture scales linearly in both trajectory length and particle count, STFlow uses about 1.9 times less time and 1.56 times less memory than the compared generative baselines on long trajectories.

Reading between the lines

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

  • The same data-dependent coupling recipe should transfer to other conditional generation settings, such as inpainting, super-resolution, or endpoint-conditioned generation, because the prior construction works for arbitrary observed timesteps, which the paper leaves as future work.
  • The transport-cost rationale predicts a measurable correlation: across datasets, the reduction in mean $\|x_1 - x_0\|$ from using the informed prior versus a Gaussian should track the accuracy gain, so datasets with little reduction should show little benefit.
  • Replacing the random walk with a periodic or constrained stochastic process that is still cheap to sample should extend STFlow to systems with periodicity or hard constraints, the failure modes the authors acknowledge.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. STFlow is a conditional flow-matching model for fixed-length geometric trajectories. It constructs a data-dependent prior: the observed frames are kept fixed, and the future frames are initialized by a random walk whose drift and per-particle velocity variance are estimated from the observed segment (Eq. 2). A permutation-equivariant EGCL plus a temporal UNet (or Transformer) parameterizes the flow-matching vector field, trained with the conditional flow-matching loss (Eq. 3), and inference uses 5 Euler steps. The paper evaluates on N-body systems, MD17 molecules, and NBA player trajectories, with ablations on the prior and architecture plus scaling measurements.

Significance. The underlying idea is timely and sensible: replacing an isotropic Gaussian prior with a random-walk prior conditioned on observed frames reduces the transport cost that the learned vector field must cover, and the ablation in §4.4 shows large gains over naive Gaussian and partial couplings. The authors also make concrete methodological contributions, including explicit training/inference algorithms in Appendix A.1, a time-shift- and permutation-equivariant architecture, and a clean mechanism story. If the numbers are reproducible and the claims are appropriately scoped, STFlow would be a useful efficiency-oriented alternative to GeoTDM and LaM-SLidE. However, the paper currently asserts universal SOTA accuracy that its own experimental tables do not support, and the evaluation lacks error bars and reruns of baselines, so the strength of the empirical contribution cannot be fully assessed yet.

major comments (3)
  1. [Abstract and §5] The abstract's claim of 'lowest prediction errors' and the conclusion's 'consistent improvements' are not supported by the reported tables. In the MD17 results table, LaM-SLidE outperforms STFlow on Aspirin (ADE/FDE 0.059/0.098 vs 0.076/0.142) and on Uracil (0.050/0.074 vs 0.050/0.079), so the statement in §4.1.2 that STFlow achieves the lowest errors across 7 of 8 molecules is inaccurate (it is 6 of 8). In the NBA setup-2 table, STFlow's min20 ADE/FDE of 0.99/1.68 is worse than MoFlow (0.71/0.86) and LED (0.81/1.10), although STFlow wins on mean20. The universal 'lowest' claim should be replaced by per-benchmark, per-metric statements, or the experiments should be extended to support it.
  2. [§4.1 and Tables 2-5] The main quantitative claims lack uncertainty quantification. Tables 2, 3, and 5 report averages over 5 runs but no standard deviations or confidence intervals, and the NBA table reports no run statistics. Since many baseline numbers are quoted from other papers (marked with *), small margins cannot be assessed. The authors should report variance or confidence intervals, state explicitly which baselines are cited rather than reproduced, and ideally rerun baselines under identical splits and preprocessing.
  3. [§3.3 and §4.1.1/4.1.2] The complexity analysis mismatches the actual graph connectivity used in the experiments. The forward-pass complexity is derived as O(L(|E|d^2 + N T d^2)) = O(L N T d^2) by invoking fixed-distance-threshold connectivity, but §4.1.1 states that particles are represented as fully connected dynamic graphs and §4.1.2 states that MD17 also uses a fully connected graph. With full connectivity, |E| = O(N^2) per timestep, giving O(L N^2 T d^2), not linear in N. Moreover, the scaling experiment in §4.3 fixes N=21 and only varies T, so it does not substantiate 'linear scaling in number of particles'. Please correct the stated complexity or use a genuinely sparse graph in experiments.
minor comments (4)
  1. [§4.1.2 and §4.1.3] The in-text table references are inconsistent: §4.1.2 refers to 'Table 2' for the MD17 results, but the compiled MD17 table is captioned Table 3, while §4.1.3 refers to 'Table 3' for the NBA results, but that table is captioned Table 4. Please fix all cross-references.
  2. [§4.1.1 and Eq. (3)] The text says the model predicts 'a vector field of velocities', but Eq. (3) and Algorithm 1 define the regression target as u = x1 - x0, which is a position-space displacement. Please clarify whether the network output is a velocity or a coordinate displacement, and align the terminology.
  3. [Table 5] The third prior row in Table 5 is labeled 'Coupled, p0, s=1 (2)'; this label appears to contain a typo and should be cleaned up.
  4. [Appendix A.3, Table 7] The column header 'τ distributions lr' is garbled, and the learning rate entries such as '45·10−4' are hard to parse; please reformat the table so that the τ distribution and learning rate are clearly separated.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the informed prior is built from conditioning frames only, and the performance claims are empirical and checkable against the reported tables.

full rationale

The paper's load-bearing mechanism, the data-dependent random-walk prior, is defined in Eq. 2 as zeta_t = zeta_{t-1} + mu + sigma_o * z_t with zeta_{c-1} = x^{c-1}, where mu and sigma_o are computed only from the observed frames x_{0:c}. The coupling construction in Sec. 3.2 sets m(x_1) = [x_1^0, ..., x_1^{c-1}, 0, ..., 0], so the future target x_{c:T} is not used to build the prior; this is a genuine coupling from conditioning information rather than a target-derived fit. The training objective in Eq. 3 supervises v_theta against the true displacement x_1 - x_0, so no fitted parameter is renamed as a prediction, and the reported ADE/FDE metrics are computed on generated trajectories, not on quantities that appear in the loss. The claimed transport-cost reduction is a designed property of the prior (quantified by the measured mean ||u|| in the ablation table), not an independent prediction derived from the model. The ablation results 1-2 (85% and 74% error increases without coupling) and the prior-only rows in Tables 2-4, which are far worse than STFlow's errors, confirm that the learned flow performs the prediction rather than the prior itself. The only self-citations (Minartz et al. 2023, 2025) appear in related-work context and are not load-bearing for any derivation. The abstract's claim of 'lowest prediction errors' is not fully supported by the paper's own tables - LaM-SLidE beats STFlow on MD17 Aspirin and Uracil, and MoFlow/LED beat STFlow on NBA setup-2 min20 - but an overstated empirical claim is a correctness/accuracy issue, not circular reasoning. No step in the claimed derivation chain reduces to its own inputs by construction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on flow matching theory (standard), the data-dependent coupling framework (standard), and the domain assumption that observed-window velocity statistics predict future statistics. The prior's drift and variance are fitted to conditioning frames, which is legitimate but introduces a hyperparameter s and a tuned tau distribution.

free parameters (2)
  • s = 4 (default; tuned per dataset)
    Scale factor multiplying the velocity variance in the random-walk prior (Eq. 2). Ablation 3 in Table 5 compares s=1 vs s=4; the authors state the influence is dataset-specific, so s is a tuned hyperparameter.
  • alpha (tau distribution exponent) = 0.5
    Exponent in the U[0,1]^alpha distribution for sampling tau in the flow matching loss (Sec. 3.2). The authors selected alpha=0.5 after observing better performance, so it is a fitted hyperparameter.
assumptions (4)
  • standard math Conditional flow matching loss L_CFM equals the marginal flow matching loss for any coupling (Lipman et al., 2023; Liu et al., 2023).
    Invoked in Sec. 3.2 to train v_theta with loss (3). This is a standard theorem, not proved in the paper.
  • standard math A data-dependent coupling pi(x0|x1) defines a valid prior p0(x0) = integral pi(x0|x1) p1(x1) dx1 (Albergo et al., 2024).
    Used in Sec. 3.2 to construct the informed prior. Standard framework from cited work.
  • domain assumption The future trajectory xc:T follows a random walk with drift mu and velocity variance sigma_o estimated from the observed frames x0:c (Eq. 2).
    This is the key modeling assumption (Eq. 2, Sec. 3.2). The paper itself notes limitations for periodic systems, strong external influences, or hard constraints.
  • domain assumption Baseline performance numbers reported in Tables 2-4 from prior papers (Han et al., 2024; Xu et al., 2022b; etc.) were obtained under the same data splits, conditioning windows, and metrics as STFlow.
    Comparisons rely on published baseline numbers rather than a unified re-implementation, a common but untested assumption.

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Cite this review

Pith. "Pith review of STFlow: Data-Coupled Flow Matching for Geometric Trajectory Simulation." pith.science (2026). https://pith.science/paper/ZZ2GS6XZ

@misc{pith2026250518647,
  author       = {Pith},
  title        = {Pith review of: STFlow: Data-Coupled Flow Matching for Geometric Trajectory Simulation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZZ2GS6XZ}},
  note         = {Machine review of arXiv:2505.18647}
}
read the original abstract

Simulating trajectories of dynamical systems is a fundamental problem in a wide range of fields such as molecular dynamics, biochemistry, and pedestrian dynamics. Machine learning has become an invaluable tool for scaling physics-based simulators and developing models directly from experimental data. In particular, recent advances in deep generative modeling and geometric deep learning enable probabilistic simulation by learning complex trajectory distributions while respecting intrinsic permutation and time-shift symmetries. However, trajectories of N-body systems are commonly characterized by high sensitivity to perturbations leading to bifurcations, as well as multi-scale temporal and spatial correlations. To address these challenges, we introduce STFlow (Spatio-Temporal Flow), a generative model based on graph neural networks and hierarchical convolutions. By incorporating data-dependent couplings within the Flow Matching framework, STFlow denoises starting from conditioned random-walks instead of Gaussian noise. This novel informed prior simplifies the learning task by reducing transport cost, increasing training and inference efficiency. We validate our approach on N-body systems, molecular dynamics, and human trajectory forecasting. Across these benchmarks, STFlow achieves the lowest prediction errors with fewer simulation steps and improved scalability.

Figures

Figures reproduced from arXiv: 2505.18647 by the authors.

Figure 1
Figure 1. Overview of STFlow. Given trajectories x1 ∼ p1, we construct a noisy prior x0 informed by the observed initial conditions and predict a vector field vθ using repeating layers of spatial message passing and temporal convolution. given h and E: p1(x | h, E) = p1(x c:T | x 0:c , h, E) p1(x 0:c | h 0:c , E 0:c ) (1) In the simulation problem setting, we presuppose that an initial part of the trajectory x 0:c is provided… view at source ↗
Figure 2
Figure 2. Inference results on the N-Body gravity dataset. The black dots represent the 10 conditioning steps, the colored dots are the 20 generated steps [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Velocity and acceleration density estimates from the 20 predicted and ground truth frames of the MD17 Ethanol test set (n = 216320) 4.2. Density evaluation To assess whether STFlow accurately captures the distribu￾tional structure of trajectory dynamics beyond point-wise prediction errors, we compare the simulated and ground￾truth densities of position-based features for the MD17 Ethanol test set results, shown in … view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Scaling experiments on the MD17 Aspirin dataset. Time per training steps (s) and max. allocated GPU memory (GB) are measured for increasing trajectory length. Both axis are log-scaled. discrepancy in the FDE metric on the NBody Gravity dataset. Results can be seen in …
Figure 5
Figure 5. Figure 5: Density evaluation of velocities and accelerations from the Gravity test set inference trajectories 15 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: Density evaluation of velocities and accelerations from the NBA Score test set inference trajectories [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: Trajectory inference results from the N-body Springs test set 16 [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: Trajectory inference results from the N-body Charged test set [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]
Figure 9
Figure 9. Figure 9: Aspirin (left) and Benzene (right) trajectory inference results from the MD17 test set [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Ethanol (left) and Malonaldehyde (right) trajectory inference results from the MD17 test set 17 [PITH_FULL_IMAGE:figures/full_fig_p017_10.png]
Figure 11
Figure 11. Figure 11: Naphthalene (left) and Salicylic (right) trajectory inference results from the MD17 test set [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]
Figure 12
Figure 12. Figure 12: Toluene (left) and Uracil (right) trajectory inference results from the MD17 test set 18 [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]

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Reference graph

Works this paper leans on

60 extracted references · 38 canonical work pages · cited by 1 Pith paper

  1. [1]

    Albergo, Mark Goldstein, Nicholas Matthew Boffi, Rajesh Ranganath, and Eric Vanden-Eijnden

    Michael S. Albergo, Mark Goldstein, Nicholas Matthew Boffi, Rajesh Ranganath, and Eric Vanden-Eijnden. Stochastic Interpolants with Data - Dependent Couplings . In International Conference on Machine Learning ( ICML ) , 2024

    work page 2024

  2. [2]

    Social ways: Learning multi-modal distributions of pedestrian trajectories with gans

    Javad Amirian, Jean-Bernard Hayet, and Julien Pettre. Social ways: Learning multi-modal distributions of pedestrian trajectories with gans. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, June 2019

    work page 2019

  3. [3]

    Interaction networks for learning about objects, relations and physics

    Peter Battaglia, Razvan Pascanu, Matthew Lai, Danilo Jimenez Rezende, and koray kavukcuoglu. Interaction networks for learning about objects, relations and physics. In D. Lee, M. Sugiyama, U. Luxburg, I. Guyon, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 29. Curran Associates, Inc., 2016. URL https://proceedings.neur...

    work page 2016

  4. [4]

    Erik J Bekkers, Sharvaree Vadgama, Rob Hesselink, Putri A Van der Linden, and David W. Romero. Fast, expressive \ mathrm\ SE \ (n)\ equivariant networks through weight-sharing in position-orientation space. In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=dPHLbUqGbr

    work page 2024

  5. [5]

    Geometric and physical quantities improve e(3) equivariant message passing, 2022 a

    Johannes Brandstetter, Rob Hesselink, Elise van der Pol, Erik J Bekkers, and Max Welling. Geometric and physical quantities improve e(3) equivariant message passing, 2022 a . URL https://arxiv.org/abs/2110.02905

    arXiv 2022

  6. [6]

    Worrall, and Max Welling

    Johannes Brandstetter, Daniel E. Worrall, and Max Welling. Message passing neural PDE solvers. In International Conference on Learning Representations, 2022 b . URL https://openreview.net/forum?id=vSix3HPYKSU

    work page 2022

  7. [7]

    The gravitational billion body problem

    Jeroen B é dorf. The gravitational billion body problem. PhD thesis, F aculty of S cience, L eiden U niversity, 2014

    work page 2014

  8. [8]

    DY ffusion: A dynamics-informed diffusion model for spatiotemporal forecasting

    Salva R \"u hling Cachay, Bo Zhao, Hailey Joren, and Rose Yu. DY ffusion: A dynamics-informed diffusion model for spatiotemporal forecasting. In Thirty-seventh Conference on Neural Information Processing Systems, 2023. URL https://openreview.net/forum?id=WRGldGm5Hz

    work page 2023

Show all 60 references
  1. [9]

    Sauceda, Igor Poltavsky, Kristof T

    Stefan Chmiela, Alexandre Tkatchenko, Huziel E. Sauceda, Igor Poltavsky, Kristof T. Schütt, and Klaus-Robert Müller. Machine learning of accurate energy-conserving molecular force fields. Science Advances, 3 0 (5), May 2017. ISSN 2375-2548. doi:10.1126/sciadv.1603015. URL http...

    2017 doi

  2. [10]

    Discovering symbolic models from deep learning with inductive biases

    Miles Cranmer, Alvaro Sanchez Gonzalez, Peter Battaglia, Rui Xu, Kyle Cranmer, David Spergel, and Shirley Ho. Discovering symbolic models from deep learning with inductive biases. In H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, editors, Advances in Neural In...

    2020

  3. [11]

    Point cloud approach to generative modeling for galaxy surveys at the field level

    Carolina Cuesta-Lazaro and Siddharth Mishra-Sharma. Point cloud approach to generative modeling for galaxy surveys at the field level. Physical Review D, 109 0 (12): 0 123531, 2024

    2024

  4. [12]

    Diffusion models beat gans on image synthesis, 2021

    Prafulla Dhariwal and Alex Nichol. Diffusion models beat gans on image synthesis, 2021. URL https://arxiv.org/abs/2105.05233

    2021 arXiv

  5. [13]

    Fuchs, Daniel E

    Fabian B. Fuchs, Daniel E. Worrall, Volker Fischer, and Max Welling. Se(3)-transformers: 3d roto-translation equivariant attention networks, 2020. URL https://arxiv.org/abs/2006.10503

    2020 arXiv

  6. [14]

    Deep learning for dynamic graphs: models and benchmarks

    Alessio Gravina and Davide Bacciu. Deep learning for dynamic graphs: models and benchmarks. IEEE Transactions on Neural Networks and Learning Systems, 2024

    2024

  7. [15]

    Stochastic trajectory prediction via motion indeterminacy diffusion

    Tianpei Gu, Guangyi Chen, Junlong Li, Chunze Lin, Yongming Rao, Jie Zhou, and Jiwen Lu. Stochastic trajectory prediction via motion indeterminacy diffusion. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17113--17122, 2022 a

    2022

  8. [16]

    Stochastic trajectory prediction via motion indeterminacy diffusion, 2022 b

    Tianpei Gu, Guangyi Chen, Junlong Li, Chunze Lin, Yongming Rao, Jie Zhou, and Jiwen Lu. Stochastic trajectory prediction via motion indeterminacy diffusion, 2022 b . URL https://arxiv.org/abs/2203.13777

    2022 arXiv

  9. [17]

    Social gan: Socially acceptable trajectories with generative adversarial networks, 2018

    Agrim Gupta, Justin Johnson, Li Fei-Fei, Silvio Savarese, and Alexandre Alahi. Social gan: Socially acceptable trajectories with generative adversarial networks, 2018. URL https://arxiv.org/abs/1803.10892

    2018 arXiv

  10. [18]

    Learning modular simulations for homogeneous systems

    Jayesh Gupta, Sai Vemprala, and Ashish Kapoor. Learning modular simulations for homogeneous systems. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 14852--14864. Curran Associat...

    2022

  11. [19]

    Geometric Trajectory Diffusion Models

    Jiaqi Han, Minkai Xu, Aaron Lou, Haotian Ye, and Stefano Ermon. Geometric Trajectory Diffusion Models . In The Thirty -eighth Annual Conference on Neural Information Processing Systems , 2024

    2024

  12. [20]

    Douglas C. Heggie. The gravitational million-body problem. Symposium - International Astronomical Union, 208: 0 81–92, 2003. doi:10.1017/S0074180900207043

    2003 doi

  13. [21]

    Denoising diffusion probabilistic models

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 6840--6851. Curran Associates, Inc., 2020. URL h...

    2020

  14. [22]

    Kingma, Ben Poole, Mohammad Norouzi, David J

    Jonathan Ho, William Chan, Chitwan Saharia, Jay Whang, Ruiqi Gao, Alexey Gritsenko, Diederik P. Kingma, Ben Poole, Mohammad Norouzi, David J. Fleet, and Tim Salimans. Imagen video: High definition video generation with diffusion models, 2022. URL https://arxiv.org/abs/2210.02303

    2022 arXiv

  15. [23]

    Gritsenko, Jasmijn Bastings, Ben Poole, Rianne van den Berg, and Tim Salimans

    Emiel Hoogeboom, Alexey A. Gritsenko, Jasmijn Bastings, Ben Poole, Rianne van den Berg, and Tim Salimans. Autoregressive diffusion models. In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=Lm8T39vLDTE

    2022

  16. [24]

    Neural relational inference for interacting systems, 2018

    Thomas Kipf, Ethan Fetaya, Kuan-Chieh Wang, Max Welling, and Richard Zemel. Neural relational inference for interacting systems, 2018. URL https://arxiv.org/abs/1802.04687

    2018 arXiv

  17. [25]

    Equivariant flow matching

    Leon Klein, Andreas Kr \"a mer, and Frank Noe. Equivariant flow matching. In Thirty-seventh Conference on Neural Information Processing Systems, 2023. URL https://openreview.net/forum?id=eLH2NFOO1B

    2023

  18. [26]

    Benchmarking autoregressive conditional diffusion models for turbulent flow simulation, 2024

    Georg Kohl, Li-Wei Chen, and Nils Thuerey. Benchmarking autoregressive conditional diffusion models for turbulent flow simulation, 2024. URL https://arxiv.org/abs/2309.01745

    2024 arXiv

  19. [27]

    W. Kohn, A. D. Becke, and R. G. Parr. Density functional theory of electronic structure. The Journal of Physical Chemistry, 100 0 (31): 0 12974--12980, 1996. doi:10.1021/jp960669l. URL https://doi.org/10.1021/jp960669l

    1996 doi

  20. [28]

    Rediscovering orbital mechanics with machine learning

    Pablo Lemos, Niall Jeffrey, Miles Cranmer, Shirley Ho, and Peter Battaglia. Rediscovering orbital mechanics with machine learning. Machine Learning: Science and Technology, 4 0 (4): 0 045002, oct 2023. doi:10.1088/2632-2153/acfa63. URL https://dx.doi.org/10.1088/2632-2153/acfa63

    2023 doi

  21. [29]

    Crowds by example

    Alon Lerner, Yiorgos Chrysanthou, and Dani Lischinski. Crowds by example. Computer Graphics Forum, 26 0 (3): 0 655--664, 2007. doi:https://doi.org/10.1111/j.1467-8659.2007.01089.x. URL https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-8659.2007.01089.x

    2007

  22. [30]

    Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, and Matthew Le. Flow Matching for Generative Modeling . In International Conference on Learning Representations ( ICLR ) , 2023

    2023

  23. [31]

    Pde-refiner: Achieving accurate long rollouts with neural pde solvers

    Phillip Lippe, Bas Veeling, Paris Perdikaris, Richard Turner, and Johannes Brandstetter. Pde-refiner: Achieving accurate long rollouts with neural pde solvers. In Advances in Neural Information Processing Systems, volume 36, pages 67398--67433. Curran Associates, Inc., 2023. U...

    2023

  24. [32]

    HOPE : High-order graph ODE for modeling interacting dynamics

    Xiao Luo, Jingyang Yuan, Zijie Huang, Huiyu Jiang, Yifang Qin, Wei Ju, Ming Zhang, and Yizhou Sun. HOPE : High-order graph ODE for modeling interacting dynamics. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett, editors,...

    2023

  25. [33]

    PGODE : Towards high-quality system dynamics modeling

    Xiao Luo, Yiyang Gu, Huiyu Jiang, Hang Zhou, Jinsheng Huang, Wei Ju, Zhiping Xiao, Ming Zhang, and Yizhou Sun. PGODE : Towards high-quality system dynamics modeling. In Forty-first International Conference on Machine Learning, 2024. URL https://openreview.net/forum?id=jrE7geZekq

    2024

  26. [34]

    It is not the journey but the destination: Endpoint conditioned trajectory prediction, 2020

    Karttikeya Mangalam, Harshayu Girase, Shreyas Agarwal, Kuan-Hui Lee, Ehsan Adeli, Jitendra Malik, and Adrien Gaidon. It is not the journey but the destination: Endpoint conditioned trajectory prediction, 2020. URL https://arxiv.org/abs/2004.02025

    2020 arXiv

  27. [35]

    Leapfrog diffusion model for stochastic trajectory prediction

    Weibo Mao, Chenxin Xu, Qi Zhu, Siheng Chen, and Yanfeng Wang. Leapfrog diffusion model for stochastic trajectory prediction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5517--5526, 2023

    2023

  28. [36]

    Koop, and Vlado Menkovski

    Koen Minartz, Yoeri Poels, Simon M. Koop, and Vlado Menkovski. Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamics . In Conference on Neural Information Processing Systems ( NeurIPS ) , 2023

    2023

  29. [37]

    Discovering interaction mechanisms in crowds via deep generative surrogate experiments

    Koen Minartz, Fleur Hendriks, Simon Martinus Koop, Alessandro Corbetta, and Vlado Menkovski. Discovering interaction mechanisms in crowds via deep generative surrogate experiments. Scientific Reports, 15 0 (1): 0 10385, 2025

    2025

  30. [38]

    Newtonian scene understanding: Unfolding the dynamics of objects in static images

    Roozbeh Mottaghi, Hessam Bagherinezhad, Mohammad Rastegari, and Ali Farhadi. Newtonian scene understanding: Unfolding the dynamics of objects in static images. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3521--3529, 2016

    2016

  31. [39]

    Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaos, 2025

    Chris Pedersen, Laure Zanna, and Joan Bruna. Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaos, 2025. URL https://arxiv.org/abs/2503.18731

    2025 arXiv

  32. [40]

    Pellegrini, A

    S. Pellegrini, A. Ess, K. Schindler, and L. van Gool. You'll never walk alone: Modeling social behavior for multi-target tracking. In 2009 IEEE 12th International Conference on Computer Vision, pages 261--268, 2009. doi:10.1109/ICCV.2009.5459260

    2009

  33. [41]

    Clifford group equivariant neural networks

    David Ruhe, Johannes Brandstetter, and Patrick Forr \'e . Clifford group equivariant neural networks. In Thirty-seventh Conference on Neural Information Processing Systems, 2023. URL https://openreview.net/forum?id=n84bzMrGUD

    2023

  34. [42]

    Rolling diffusion models

    David Ruhe, Jonathan Heek, Tim Salimans, and Emiel Hoogeboom. Rolling diffusion models. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp, editors, Proceedings of the 41st International Conference on Ma...

    2024

  35. [43]

    Deepar: Probabilistic forecasting with autoregressive recurrent networks

    David Salinas, Valentin Flunkert, Jan Gasthaus, and Tim Januschowski. Deepar: Probabilistic forecasting with autoregressive recurrent networks. International Journal of Forecasting, 36 0 (3): 0 1181--1191, 2020. ISSN 0169-2070. doi:https://doi.org/10.1016/j.ijforecast.2019.07....

    2020 doi

  36. [44]

    Trajectron++: Dynamically-feasible trajectory forecasting with heterogeneous data, 2021

    Tim Salzmann, Boris Ivanovic, Punarjay Chakravarty, and Marco Pavone. Trajectron++: Dynamically-feasible trajectory forecasting with heterogeneous data, 2021. URL https://arxiv.org/abs/2001.03093

    2021 arXiv

  37. [45]

    Learning to simulate complex physics with graph networks

    Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Peter Battaglia. Learning to simulate complex physics with graph networks. In Hal Daumé III and Aarti Singh, editors, Proceedings of the 37th International Conference on Machine Learning, volu...

    2020

  38. [46]

    E(n) Equivariant Graph Neural Networks

    Victor Garcia Satorras, Emiel Hoogeboom, and Max Welling. E(n) Equivariant Graph Neural Networks . In International Conference on Machine Learning ( ICML ) , pages 9323--9332, 2021

    2021

  39. [47]

    Improved sampling of diffusion models in fluid dynamics with tweedie's formula

    Youssef Shehata, Benjamin Holzschuh, and Nils Thuerey. Improved sampling of diffusion models in fluid dynamics with tweedie's formula. In The Thirteenth International Conference on Learning Representations, 2025. URL https://openreview.net/forum?id=0FbzC7B9xI

    2025

  40. [48]

    Turner, and Emile Mathieu

    Aliaksandra Shysheya, Cristiana Diaconu, Federico Bergamin, Paris Perdikaris, Jos\' e Miguel Hern\' a ndez-Lobato, Richard E. Turner, and Emile Mathieu. On conditional diffusion models for pde simulations. In A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak,...

    2024

  41. [49]

    Deep unsupervised learning using nonequilibrium thermodynamics

    Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. In Francis Bach and David Blei, editors, Proceedings of the 32nd International Conference on Machine Learning, volume 37 of Proceedings o...

    2015

  42. [51]

    Smidt, Steven Kearnes, Lusann Yang, Li Li, Kai Kohlhoff, and Patrick Riley

    Nathaniel Thomas, Tess E. Smidt, Steven Kearnes, Lusann Yang, Li Li, Kai Kohlhoff, and Patrick Riley. Tensor field networks: Rotation- and translation-equivariant neural networks for 3d point clouds. CoRR, abs/1802.08219, 2018 b . URL http://arxiv.org/abs/1802.08219

    2018 arXiv

  43. [52]

    Thompson, H

    Aidan P. Thompson, H. Metin Aktulga, Richard Berger, Dan S. Bolintineanu, W. Michael Brown, Paul S. Crozier, Pieter J. in 't Veld , Axel Kohlmeyer, Stan G. Moore, Trung Dac Nguyen, Ray Shan, Mark J. Stevens, Julien Tranchida, Christian Trott, and Steven J. Plimpton. Lammps - a...

    2022

  44. [53]

    Huguet, Yanlei Zhang, Jarrid Rector-Brooks, Kilian Fatras, Guy Wolf, and Y

    Alexander Tong, Nikolay Malkin, G. Huguet, Yanlei Zhang, Jarrid Rector-Brooks, Kilian Fatras, Guy Wolf, and Y. Bengio. Improving and Generalizing Flow - Based Generative Models with Minibatch Optimal Transport . In ICML Workshop on New Frontiers in Learning , Control , and Dyn...

    2023

  45. [54]

    Pixel recurrent neural networks

    A \"a ron Van Den Oord, Nal Kalchbrenner, and Koray Kavukcuoglu. Pixel recurrent neural networks. In International conference on machine learning, pages 1747--1756. PMLR, 2016

    2016

  46. [55]

    Diffstg: Probabilistic Spatio - Temporal Graph Forecasting with Denoising Diffusion Models

    Haomin Wen, Youfang Lin, Yutong Xia, Huaiyu Wan, Qingsong Wen, Roger Zimmermann, and Yuxuan Liang. Diffstg: Probabilistic Spatio - Temporal Graph Forecasting with Denoising Diffusion Models . In ACM SIGSPATIAL International Conference on Advances in Geographic Information Syst...

    2023

  47. [56]

    Equivariant spatio-temporal attentive graph networks to simulate physical dynamics, 2024

    Liming Wu, Zhichao Hou, Jirui Yuan, Yu Rong, and Wenbing Huang. Equivariant spatio-temporal attentive graph networks to simulate physical dynamics, 2024. URL https://arxiv.org/abs/2405.12868

    2024 arXiv

  48. [57]

    Tan, Yuhong Tan, Siheng Chen, Yu Guang Wang, Xinchao Wang, and Yanfeng Wang

    Chenxin Xu, Robby T. Tan, Yuhong Tan, Siheng Chen, Yu Guang Wang, Xinchao Wang, and Yanfeng Wang. Eqmotion: Equivariant multi-agent motion prediction with invariant interaction reasoning, 2023. URL https://arxiv.org/abs/2303.10876

    2023 arXiv

  49. [58]

    SocialVAE: Human Trajectory Prediction Using Timewise Latents, page 511–528

    Pei Xu, Jean-Bernard Hayet, and Ioannis Karamouzas. SocialVAE: Human Trajectory Prediction Using Timewise Latents, page 511–528. Springer Nature Switzerland, 2022. ISBN 9783031197727. doi:10.1007/978-3-031-19772-7_30. URL http://dx.doi.org/10.1007/978-3-031-19772-7_30

    2022 doi

  50. [59]

    Consistency flow matching: Defining straight flows with velocity consistency, 2024

    Ling Yang, Zixiang Zhang, Zhilong Zhang, Xingchao Liu, Minkai Xu, Wentao Zhang, Chenlin Meng, Stefano Ermon, and Bin Cui. Consistency flow matching: Defining straight flows with velocity consistency, 2024. URL https://arxiv.org/abs/2407.02398

    2024 arXiv

  51. [60]

    Bitrap: Bi-directional pedestrian trajectory prediction with multi-modal goal estimation, 2020

    Yu Yao, Ella Atkins, Matthew Johnson-Roberson, Ram Vasudevan, and Xiaoxiao Du. Bitrap: Bi-directional pedestrian trajectory prediction with multi-modal goal estimation, 2020. URL https://arxiv.org/abs/2007.14558

    2020 arXiv

  52. [61]

    Learning interacting dynamical systems with latent gaussian process ODE s

    Cagatay Yildiz, Melih Kandemir, and Barbara Rakitsch. Learning interacting dynamical systems with latent gaussian process ODE s. In Alice H. Oh, Alekh Agarwal, Danielle Belgrave, and Kyunghyun Cho, editors, Advances in Neural Information Processing Systems, 2022. URL https://o...

    2022

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.