Pith. sign in

REVIEW 3 major objections 5 minor 61 references

Force Matching with Relativistic Constraints: A Physics-Inspired Approach to Stable and Efficient Generative Modeling

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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

Pith's one-line read This paper proposes Force Matching (ForM), a generative framework in which a network learns a relativistic force field instead of a velocity field, and proves that the induced sampling ODE keeps particle speed below the speed of light $c$…

desk verdict A novel relativistic-force framing for flow matching, but the empirical evidence is circular and the sampling algorithms as written are inconsistent. read the letter →

arxiv 2502.08150 v1 pith:YMGJTIKE submitted 2025-02-12 cs.LG cs.AIcs.CV

Yang Cao , Bo Chen , Xiaoyu Li , Yingyu Liang , Zhizhou Sha , Zhenmei Shi , Zhao Song , Mingda Wan This is my paper · ORCID
classification cs.LGcs.AIcs.CV
keywords forcematchinggenerativemodelingspecialrelativityLorentzfactorflowvelocityconstraintsamplingstabilitysecond-orderODE
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 Force Matching (ForM), a generative modeling framework that replaces the velocity-matching objective of flow matching with a force-matching objective drawn from special relativity. Because the Lorentz factor appears in the force law, the speed of light $c$ becomes a hard upper bound on sample velocity, and the paper proves that this bound is preserved along the entire sampling trajectory. On toy datasets whose target distributions are generated by Lorentz force fields, ForM reports much lower Euclidean distance loss than first-order and first-plus-second-order flow matching, for example 0.714 versus 5.853 on half-moons. The reason to care is stability: flow-based samplers can develop unbounded velocities, and a provable speed cap removes that failure mode.

What carries the argument

The load-bearing object is the Lorentz factor $\gamma_t = (1 - \|\dot{x}_t\|_2^2/c^2)^{-1/2}$ together with the relativistic force definition $f_t = m(\gamma_t \ddot{x}_t + \gamma_t^3 \langle \dot{x}_t, \ddot{x}_t\rangle/c^2\, \dot{x}_t)$. The sampling ODE in Theorem A.1 inverts that force relation to produce an acceleration, and the speed-derivative identity from Lemma A.2 turns $c$ into a repulsive barrier: as $\|\dot{x}_t\|_2$ approaches $c$, the factor $(1 - \|\dot{x}_t\|_2^2/c^2)$ drives the squared speed back down. When the interpolation path is chosen as $\alpha_t = \sin t$, $\sigma_t = \cos t$, the same force law yields the closed-form force interpolation of Theorem 4.4.

What would settle it

Train ForM and the first-order and first-plus-second-order flow matching baselines on a standard generative benchmark whose target distribution is not produced by a Lorentz field, such as CIFAR-10 image generation, and compare sample quality (for example FID) while recording the maximum observed $\|\dot{x}_t\|_2$ during sampling. If the baselines match or beat ForM there, or if the numerical speed exceeds $c$, the broad claims of superiority and guaranteed stability are contradicted.

Watch

Extended reading notes

Core claim

The central claim is that writing the generative transport as a special-relativistic force, rather than a velocity, converts sampling into a second-order ODE with a built-in speed limit. Concretely, with interpolation $x_t = \alpha_t x_1 + \sigma_t x_0$ and Lorentz factor $\gamma_t = (1 - \|\dot{x}_t\|_2^2/c^2)^{-1/2}$, the local force is $f_t = m(\gamma_t \ddot{x}_t + \gamma_t^3 \langle \dot{x}_t, \ddot{x}_t\rangle/c^2\, \dot{x}_t)$, and the sampling ODE (Theorem A.1) is $\ddot{x}_t = \frac{1}{m\gamma_t}(f_t - \frac{\langle \dot{x}_t, f_t\rangle}{c^2}\dot{x}_t)$. The paper proves in Theorem 4.3 that every ForM sampling path satisfies $\|\dot{x}_t\|_2 < c$ for all $t \in [0,T)$. The proof hinges on the identity $\frac{d}{dt}(\frac{1}{2}\|\dot{x}_t\|_2^2) = \frac{\langle f_t, \dot{x}_t\rangle}{m\gamma_t}(1 - \|\dot{x}_t\|_2^2/c^2)$, which makes the speed cap self-enforcing. Empirically the paper reports that ForM fits the Lorentz-generated toy targets far more accurately than either baseline.

Load-bearing premise

The empirical case assumes the target datasets are manufactured by exactly the Lorentz force field that ForM is trained to match, so the reported superiority may show that ForM recognizes its own data generator rather than that relativistic speed limits improve generative modeling in general.

Editorial extensions

If this is right

  • A trained ForM sampler is provably confined to speeds below $c$, so a whole class of divergent-trajectory instabilities is excluded by construction.
  • Because the force objective is integrated as a second-order ODE, ForM can trace curved transport maps that a first-order velocity field would approximate only with many small steps.
  • With TrigFlow paths, the target force has a closed form, so training needs no simulation of the force along interpolants.
  • The speed-limit proof does not depend on the accuracy of the learned force field, so the bound holds even with a poorly regressed network.
  • In the reported toy experiments, ForM's Euclidean distance loss is roughly an order of magnitude lower than the baselines (0.714 vs 5.853 on half-moons), indicating the approach can fit the tested curved trajectories.

Reading between the lines

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

  • Since every target dataset in the paper is synthesized by simulating the same Lorentz force law that ForM is trained to regress, the large measured gap likely reflects a matching inductive bias; a fair test on standard benchmarks whose force field is unknown would tell whether the advantage is general.
  • The speed limit is a property of the sampling ODE, not of the trained network, so the same Lorentz-factor constraint could be added to existing flow-matching or score-based samplers as a projection step.
  • Making the speed cap $c$ time-dependent or learned per coordinate is a natural extension that would preserve the stability guarantee while allowing larger steps in smooth regions.
  • The paper's connection to TrigFlow suggests ForM may be compatible with consistency-style distillation, implying a possible few-step sampler that keeps the same velocity bound.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper introduces Force Matching (ForM), a generative modeling framework that replaces the learned velocity field of flow matching with a learned relativistic force field, and derives a second-order sampling ODE from the relativistic force law. The authors claim three contributions: a sampling ODE (Theorem 4.2/A.1), a speed-limit guarantee for sampling trajectories (Theorem 4.3/A.3), and an extension to TrigFlow interpolation (Theorem 4.4/A.4). Empirically, the paper reports that ForM achieves drastically lower Euclidean distance loss than first-order and first-plus-second-order flow matching on three synthetic datasets (Onedot, Halfmoons, Spiral), attributing the improvement to the relativistic velocity constraint. The theoretical derivations in the appendix are algebraically correct, but the main empirical claim is undermined by the experimental design, and the speed-limit theorem is largely vacuous because the sampling ODE is singular at the claimed bound.

Significance. If the empirical superiority were established on standard generative benchmarks and the speed limit translated into a practically meaningful stability guarantee, the idea of representing generative dynamics through a relativistic force field could be a modest but interesting contribution. The manuscript does provide a correct algebraic inversion of the relativistic force equation (Lemma A.5 and Theorem A.1) and a clean closed-form force interpolation for TrigFlow (Theorem A.4), which are useful reference derivations. However, the reported experimental results do not support the central claim of outperforming flow matching: every target dataset is generated by simulating a Lorentz force field whose parameters the authors chose, and ForM is trained to regress exactly that force, whereas the baselines are given only kinematic quantities. The paper also ships no code or checkpoints, so the quantitative results in Table 1 are not independently verifiable. The speed-limit theorem, while correct in its narrow statement, does not provide a meaningful stability guarantee beyond what the ODE's domain already enforces.

major comments (3)
  1. [Algorithms 5 and 6] As written, Algorithm 5 line 14 and Algorithm 6 line 9 pass only the time t to the force network F_theta, with no dependence on the current position x_t. Combined with the zero initial velocity in Algorithm 6 (v is never initialized before the loop, and Theorem 4.2 sets dot_x_0 = 0), all samples would experience the same acceleration at each timestep and hence the output distribution would be a deterministic translation of N(0, I). This cannot reproduce the Halfmoons or Spiral shapes shown in Figure 4. If the intended implementation actually conditions on x_t, the pseudocode is misleading and the experiment is not reproducible as written; either way, the manuscript does not provide the information needed to understand the reported results.
  2. [Theorem A.3 and Appendix A.2] The speed-limit theorem is vacuous in its current form. The sampling ODE in Theorem A.1 contains the factor 1/gamma_t, and gamma_t is undefined when |v_t| = c; hence the ODE itself is only defined for trajectories with |v_t| < c. The proof of Theorem A.3 shows that the derivative of X(t) = |v_t|^2/2 is non-positive at |v_t| = c, which merely confirms that the trajectory cannot cross the boundary of the ODE's domain. It does not rule out reaching |v_t| = c in finite time, nor does it address what happens if the force drives the velocity toward c (the derivative in Lemma A.2 also vanishes as |v_t| approaches c, so the argument does not establish the claimed strict inequality for all t). The stability benefit claimed for ForM therefore rests on a statement that is essentially a consequence of the ODE being undefined outside the speed bound, not a new dynamical guarantee.
  3. [Section 5.3 and Table 1] The quantitative evaluation is insufficiently specified. Table 1 reports 'Euclidean distance loss' but the manuscript does not define the metric precisely (e.g., average over samples? distance between which endpoints? units reported as '0.1 light seconds' but no conversion or normalization is given). There are no standard deviations, no number of runs, no network architecture, no optimizer or hyperparameters, and no training budget. Section 5.2 contains only qualitative trajectory plots, and Section 5.3 mentions Onedot and Halfmoons while Table 1 also reports Spiral. Without these details and without code, the reported results cannot be checked or replicated.
minor comments (5)
  1. [Throughout] The paper contains many typos and grammatical errors (e.g., 'Giving a the interpolation' in Theorem 4.4, 'we select the αt and σt identical' in Theorem 4.4, 'the speed of light is set to c = 3 × 10^8 m/s' in Section 5.1 while Theorem 4.3 uses c without units). A careful proofreading pass is needed.
  2. [Section 5.3] The text says the loss is evaluated 'on the Onedot dataset and Halfmoons dataset', but Table 1 also reports results for Spiral; the text should be updated for consistency.
  3. [Algorithms 1-4] Algorithm 3 line 13 defines the second-order loss using u2(u1(x_t, t), x_t, t), where u2 takes the predicted velocity as an argument, but this nested evaluation is not explained or motivated in the text, and it makes the baseline implementation unclear.
  4. [Section 2] The related work section contains a long string of citations described as having 'significantly inspired and influenced our work' without any specific connection to ForM; several of these citations appear unrelated to force matching or relativistic dynamics, and the passage should be trimmed or made substantive.
  5. [Figures 1-3] The captions state 'Left: ... Right: ...' but the subcaptions and the '1'/'0' labels in the figures are confusing; it is not clear which distribution is π0 and which is π1, and the color legend is not provided.

Circularity Check

3 steps flagged · score 6.0 of 10

The central empirical superiority claim is circular by construction: every toy target is generated by the same Lorentz force field that ForM is trained to regress, while the baselines never see force labels; the speed-limit guarantee is likewise built into the definition of the Lorentz factor.

  1. fitted input called prediction [Section 5.1 (Datasets), Definition 4.1, Table 1]
    "The target distribution is generated via a Lorentz field ... The parallel force is defined as γ3m0ax, while the perpendicular force follows γm0ax ... LForM(θ) := E t∼Uniform[0,T ],x1∼D [∥Ft(xt) − ft(xt)∥2 2]."

    Every synthetic target (Onedot, Halfmoons, Spiral) is produced by simulating a Lorentz force field whose parallel and perpendicular components are hand-specified by the authors. The ForM training objective regresses exactly that force ft along the simulated trajectories, and the sampling ODE in Theorem 4.2 inverts the same relativistic force law. The O1 and O1+O2 baselines are given only kinematic quantities and are never shown the force labels. Therefore the large loss gap in Table 1 measures whether ForM memorized the data-generating force field that the baselines were not asked to learn; the reported superiority is forced by the evaluation design, not evidence of a general generative advantage.

  2. self definitional [Section 3.3 Definition 3.1; Section 4.3 Theorem 4.3; Appendix A.2 proof]
    "γt := 1 q 1 − ∥vlab t ∥2 2/c2 ... Theorem 4.3 ... the velocity satisfies ∥ ˙xt∥2 < c , ∀t ∈ [0, T)."

    The speed bound is an input, not a prediction: the Lorentz factor is defined with sqrt(1 − ||v||^2/c^2), which is only real for ||v|| < c, and this same factor is carried into the sampling ODE and then read off as Theorem 4.3. The proof re-derives dX/dt = (⟨f,v⟩/(mγ))(1 − ||v||^2/c^2) and concludes the bound, so the theorem is an algebraic restatement of the relativistic force definition. Moreover, the proof at ||v|| = c gives dX/dt = 0, so it only supports a non-strict bound even though the theorem claims strict inequality.

1 more flagged steps
  1. other [Algorithm 5 line 14; Algorithm 6 line 9; Definition 4.1; Theorem 4.2]
    "θ ← ∇θ(∥Fθ(t) − ft∥2 2) ... fL ← Fθ(t) ... where x0 ∼ N(0, I), ˙x0 = 0."

    If Algorithms 5 and 6 are read literally, the network Fθ is a function of t only and never receives the position xt, even though Definition 4.1 and Theorem 4.2 require the force at position ft(xt). With x0 ∼ N(0,I) and ˙x0 = 0, all samples then experience the same time-dependent force, so the output distribution would be a translate of the Gaussian prior and could not reproduce the reported Halfmoons or Spiral shapes. The empirical demonstration in Table 1 and Figure 4 therefore depends on an omitted position dependence that the stated algorithm does not implement, so the paper as written does not actually demonstrate the claimed transport behavior.

full rationale

The theoretical ODE derivation in Theorem A.1 is internally consistent algebra starting from Lemma A.5, and the TrigFlow force interpolation in Theorem A.4 is an algebraic consequence of the chosen interpolation, so not every step in the paper is circular. However, the two headline contributions are built-in rather than independently derived. The empirical superiority claim is circular by construction: all three toy targets are generated by a Lorentz force field specified by the authors, and ForM is trained to regress exactly that force, while the baselines never see force labels. The speed-limit guarantee is also definitional: the Lorentz factor γ = 1/sqrt(1−||v||^2/c^2) already encodes the bound, and Theorem 4.3 merely restates it through the same factor. In addition, Algorithms 5 and 6 condition Fθ only on t; if read literally, all samples share the same acceleration and the output cannot match the figures, so the empirical demonstration as written is not self-contained. No external benchmark, code, or checkpoint is provided that would break the circularity or allow the reported results to be independently reproduced. Overall score 6: partial circularity, because the central empirical and stability claims reduce to their inputs even though the formal algebra is not circular.

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

The central theoretical claim rests on the Lorentz factor definition (an input from physics) and on the assumption that the learned force field yields a well-defined ODE. The central empirical claim rests on hand-chosen force parameters used to generate the toy datasets, which makes the comparison to generic baselines favorable to ForM.

free parameters (3)
  • c (speed of light / velocity cap) = 3 × 10^8 (m/s, or scaled in toy units)
    Hand-chosen constant that defines the velocity bound; the speed-limit theorem and the training objective depend on this choice, but it is not learned from data.
  • mass m = 1 (set for simplicity)
    The paper sets m = 1 in Theorem 4.4 and uses it in the force definition; this scale is arbitrary and affects the force regression target.
  • Dataset force parameters = e.g., 1×10^7·sin(t) and 7×10^8·sin(8t) for half-moons
    The toy target distributions are generated by these hand-chosen force laws, which are exactly the values ForM is trained to predict; the reported loss numbers depend on them.
assumptions (3)
  • ad hoc to paper Generative trajectories should follow the relativistic force law f = m γ a + m γ^3 <v,a>/c^2 v
    This is the core physics-inspired modeling assumption, introduced without a principled justification for why real data distributions should evolve under special-relativistic dynamics.
  • domain assumption The sampling ODE has a unique real solution on [0,T) with ||v||<c for the learned force field
    The speed-limit proof requires the ODE to be defined, which in turn requires the velocity to stay below c; for an arbitrary neural network force, this is not guaranteed.
  • domain assumption The continuous-time speed bound transfers to the discrete Euler integrator used in Algorithm 6
    The theorem is proven for the exact ODE, but sampling uses finite steps and a learned force, so the bound may not hold in practice; the paper gives no discretization error analysis.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Force Matching with Relativistic Constraints: A Physics-Inspired Approach to Stable and Efficient Generative Modeling." pith.science (2026). https://pith.science/paper/YMGJTIKE

@misc{pith2026250208150,
  author       = {Pith},
  title        = {Pith review of: Force Matching with Relativistic Constraints: A Physics-Inspired Approach to Stable and Efficient Generative Modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YMGJTIKE}},
  note         = {Machine review of arXiv:2502.08150}
}
read the original abstract

This paper introduces Force Matching (ForM), a novel framework for generative modeling that represents an initial exploration into leveraging special relativistic mechanics to enhance the stability of the sampling process. By incorporating the Lorentz factor, ForM imposes a velocity constraint, ensuring that sample velocities remain bounded within a constant limit. This constraint serves as a fundamental mechanism for stabilizing the generative dynamics, leading to a more robust and controlled sampling process. We provide a rigorous theoretical analysis demonstrating that the velocity constraint is preserved throughout the sampling procedure within the ForM framework. To validate the effectiveness of our approach, we conduct extensive empirical evaluations. On the \textit{half-moons} dataset, ForM significantly outperforms baseline methods, achieving the lowest Euclidean distance loss of \textbf{0.714}, in contrast to vanilla first-order flow matching (5.853) and first- and second-order flow matching (5.793). Additionally, we perform an ablation study to further investigate the impact of our velocity constraint, reaffirming the superiority of ForM in stabilizing the generative process. The theoretical guarantees and empirical results underscore the potential of integrating special relativity principles into generative modeling. Our findings suggest that ForM provides a promising pathway toward achieving stable, efficient, and flexible generative processes. This work lays the foundation for future advancements in high-dimensional generative modeling, opening new avenues for the application of physical principles in machine learning.

Figures

Figures reproduced from arXiv: 2502.08150 by the authors.

Figure 1
Figure 1. Left: Onedot Dataset. The objective is to train the ForM model to learn a transport [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Left: Halfmoons Dataset. The objective is to train ForM to learn a transport trajectory [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Left: Spiral Dataset. The objective is to train the ForM model to learn a transport [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Left: Flow matching [LCBH+22] using only the first-order term. Middle: An improved method that incorporates both first- and second-order terms. Right: Our proposed ForM model applied to the Onedot, Halfmoons, and Spiral datasets. Note that the first-order method (O1) f…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

61 extracted references · 34 canonical work pages

  1. [1]

    Wasserstein gan

    Martin Arjovsky, Soumith Chintala, and L \'e on Bottou. Wasserstein gan. arXiv preprint arXiv:1701.07875 , 2017

    arXiv 2017

  2. [2]

    Language models are few-shot learners

    Tom B Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. Advances in neural information processing systems , 33:1877--1901, 2020

    work page 1901

  3. [3]

    Richspace: Enriching text-to-video prompt space via text embedding interpolation

    Yuefan Cao, Chengyue Gong, Xiaoyu Li, Yingyu Liang, Zhizhou Sha, Zhenmei Shi, and Zhao Song. Richspace: Enriching text-to-video prompt space via text embedding interpolation. arXiv preprint arXiv:2501.09982 , 2025

    arXiv 2025

  4. [4]

    Dissecting Submission Limit in Desk-Rejections: A Mathematical Analysis of Fairness in AI Conference Policies

    Yuefan Cao, Xiaoyu Li, Yingyu Liang, Zhizhou Sha, Zhenmei Shi, Zhao Song, and Jiahao Zhang. Dissecting submission limit in desk-rejections: A mathematical analysis of fairness in ai conference policies. arXiv preprint arXiv:2502.00690 , 2025

    work page Pith review arXiv 2025

  5. [5]

    Universal approximation of visual autoregressive transformers

    Yifang Chen, Xiaoyu Li, Yingyu Liang, Zhenmei Shi, and Zhao Song. Universal approximation of visual autoregressive transformers. arXiv preprint arXiv:2502.06167 , 2025

    arXiv 2025

  6. [6]

    Hsr-enhanced sparse attention acceleration

    Bo Chen, Yingyu Liang, Zhizhou Sha, Zhenmei Shi, and Zhao Song. Hsr-enhanced sparse attention acceleration. arXiv preprint arXiv:2410.10165 , 2024

    arXiv 2024

  7. [7]

    Neural ordinary differential equations

    Tian Qi Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud. Neural ordinary differential equations. In Advances in Neural Information Processing Systems (NeurIPS) , 2018

    work page 2018

  8. [8]

    Video latent flow matching: Optimal polynomial projections for video interpolation and extrapolation

    Yang Cao, Zhao Song, and Chiwun Yang. Video latent flow matching: Optimal polynomial projections for video interpolation and extrapolation. arXiv preprint arXiv:2502.00500 , 2025

    arXiv 2025

Show all 61 references
  1. [9]

    Treequestion: Assessing conceptual learning outcomes with llm-generated multiple-choice questions

    Zirui Cheng, Jingfei Xu, and Haojian Jin. Treequestion: Assessing conceptual learning outcomes with llm-generated multiple-choice questions. Proceedings of the ACM on Human-Computer Interaction , 8(CSCW2):1--29, 2024

    2024

  2. [10]

    Flownet: Learning optical flow with convolutional networks

    Alexey Dosovitskiy, Philipp Fischer, Eddy Ilg, Philip Hausser, Caner Hazirbas, Vladimir Golkov, Patrick van der Smagt, Daniel Cremers, and Thomas Brox. Flownet: Learning optical flow with convolutional networks. In IEEE International Conference on Computer Vision (ICCV) , 2015

    2015

  3. [11]

    Variational schr " odinger diffusion models

    Wei Deng, Weijian Luo, Yixin Tan, Marin Bilo s , Yu Chen, Yuriy Nevmyvaka, and Ricky TQ Chen. Variational schr " odinger diffusion models. arXiv preprint arXiv:2405.04795 , 2024

    2024 arXiv

  4. [12]

    Diffusion models beat gans on image synthesis

    Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans on image synthesis. Advances in neural information processing systems , 34:8780--8794, 2021

    2021

  5. [13]

    Efficient video prediction via sparsely conditioned flow matching

    Aram Davtyan, Sepehr Sameni, and Paolo Favaro. Efficient video prediction via sparsely conditioned flow matching. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pages 23263--23274, 2023

    2023

  6. [14]

    Zur elektrodynamik bewegter k \"o rper

    Albert Einstein et al. Zur elektrodynamik bewegter k \"o rper. Annalen der physik , 17(10):891--921, 1905

    1905

  7. [15]

    Scaling rectified flow transformers for high-resolution image synthesis

    Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas M \"u ller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, et al. Scaling rectified flow transformers for high-resolution image synthesis. In Forty-first International Conference on Mach...

    2024

  8. [16]

    How far are we from agi

    Tao Feng, Chuanyang Jin, Jingyu Liu, Kunlun Zhu, Haoqin Tu, Zirui Cheng, Guanyu Lin, and Jiaxuan You. How far are we from agi. arXiv preprint arXiv:2405.10313 , 2024

    2024 arXiv

  9. [17]

    Will Grathwohl, Ricky T. Q. Chen, Jesse Bettencourt, Ilya Sutskever, and David Duvenaud. FFJORD : Free-form continuous dynamics for scalable reversible generative models. In International Conference on Learning Representations (ICLR) , 2018

    2018

  10. [18]

    Layer compression of deep networks with straight flows

    Chengyue Gong, Xiaocong Du, Bhargav Bhushanam, Lemeng Wu, Xingchao Liu, Dhruv Choudhary, Arun Kejariwal, and Qiang Liu. Layer compression of deep networks with straight flows. In Proceedings of the AAAI Conference on Artificial Intelligence , pages 12181--12189, 2024

    2024

  11. [19]

    Generative adversarial nets

    Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in neural information processing systems , pages 2672--2680, 2014

    2014

  12. [20]

    Denoising diffusion probabilistic models

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems , 33:6840--6851, 2020

    2020

  13. [21]

    Denoising diffusion probabilistic models

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In Advances in Neural Information Processing Systems , volume 33, pages 6840--6851, 2020

    2020

  14. [22]

    On statistical rates of conditional diffusion transformers: Approximation, estimation and minimax optimality

    Jerry Yao-Chieh Hu, Weimin Wu, Yi-Chen Lee, Yu-Chao Huang, Minshuo Chen, and Han Liu. On statistical rates of conditional diffusion transformers: Approximation, estimation and minimax optimality. arXiv preprint arXiv:2411.17522 , 2024

    2024 arXiv

  15. [23]

    On statistical rates and provably efficient criteria of latent diffusion transformers (dits)

    Jerry Yao-Chieh Hu, Weimin Wu, Zhuoru Li, Sophia Pi, , Zhao Song, and Han Liu. On statistical rates and provably efficient criteria of latent diffusion transformers (dits). Advances in Neural Information Processing Systems , 38, 2024

    2024

  16. [24]

    FlowNet2 : Evolution of optical flow estimation with deep networks

    Eddy Ilg, Nikolaus Mayer, Tonmoy Saikia, Margret Keuper, Alexey Dosovitskiy, and Thomas Brox. FlowNet2 : Evolution of optical flow estimation with deep networks. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , 2017

    2017

  17. [25]

    Pyramidal flow matching for efficient video generative modeling

    Yang Jin, Zhicheng Sun, Ningyuan Li, Kun Xu, Hao Jiang, Nan Zhuang, Quzhe Huang, Yang Song, Yadong Mu, and Zhouchen Lin. Pyramidal flow matching for efficient video generative modeling. arXiv preprint arXiv:2410.05954 , 2024

    2024

  18. [26]

    Elucidating the design space of diffusion-based generative models

    Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine. Elucidating the design space of diffusion-based generative models. Advances in neural information processing systems , 35:26565--26577, 2022

    2022

  19. [27]

    Analyzing and improving the training dynamics of diffusion models

    Tero Karras, Miika Aittala, Jaakko Lehtinen, Janne Hellsten, Timo Aila, and Samuli Laine. Analyzing and improving the training dynamics of diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 24174--24184, 2024

    2024

  20. [28]

    On the translocation of masses

    Leonid Kantorovich. On the translocation of masses. Dokl. Akad. Nauk. USSR , 37:199--201, 1942

    1942

  21. [29]

    On computational limits and provably efficient criteria of visual autoregressive models: A fine-grained complexity analysis

    Yekun Ke, Xiaoyu Li, Yingyu Liang, Zhizhou Sha, Zhenmei Shi, and Zhao Song. On computational limits and provably efficient criteria of visual autoregressive models: A fine-grained complexity analysis. arXiv preprint arXiv:2501.04377 , 2025

    2025 arXiv

  22. [30]

    Circuit complexity bounds for visual autoregressive model

    Yekun Ke, Xiaoyu Li, Yingyu Liang, Zhenmei Shi, and Zhao Song. Circuit complexity bounds for visual autoregressive model. arXiv preprint arXiv:2501.04299 , 2025

    2025 arXiv

  23. [31]

    Dpbloomfilter: Securing bloom filters with differential privacy

    Yekun Ke, Yingyu Liang, Zhizhou Sha, Zhenmei Shi, and Zhao Song. Dpbloomfilter: Securing bloom filters with differential privacy. arXiv preprint arXiv:2502.00693 , 2025

    2025

  24. [32]

    Auto-encoding variational bayes

    Diederik P Kingma and Max Welling. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114 , 2013

    2013 arXiv

  25. [33]

    Flow matching for generative modeling

    Yaron Lipman, Ricky TQ Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le. Flow matching for generative modeling. arXiv preprint arXiv:2210.02747 , 2022

    2022 arXiv

  26. [34]

    Flow straight and fast: Learning to generate and transfer data with rectified flow

    Xingchao Liu, Chengyue Gong, and Qiang Liu. Flow straight and fast: Learning to generate and transfer data with rectified flow. arXiv preprint arXiv:2209.03003 , 2022

    2022 arXiv

  27. [35]

    Exploring the frontiers of softmax: Provable optimization, applications in diffusion model, and beyond

    Chenyang Li, Yingyu Liang, Zhenmei Shi, and Zhao Song. Exploring the frontiers of softmax: Provable optimization, applications in diffusion model, and beyond. arXiv preprint arXiv:2405.03251 , 2024

    2024

  28. [36]

    Simplifying, stabilizing and scaling continuous-time consistency models

    Cheng Lu and Yang Song. Simplifying, stabilizing and scaling continuous-time consistency models. arXiv preprint arXiv:2410.11081 , 2024

    2024 arXiv

  29. [37]

    Looped relu mlps may be all you need as practical programmable computers

    Yingyu Liang, Zhizhou Sha, Zhenmei Shi, Zhao Song, and Yufa Zhou. Looped relu mlps may be all you need as practical programmable computers. arXiv preprint arXiv:2410.09375 , 2024

    2024 arXiv

  30. [38]

    Multi-layer transformers gradient can be approximated in almost linear time

    Yingyu Liang, Zhizhou Sha, Zhenmei Shi, Zhao Song, and Yufa Zhou. Multi-layer transformers gradient can be approximated in almost linear time. arXiv preprint arXiv:2408.13233 , 2024

    2024 arXiv

  31. [39]

    Differential privacy mechanisms in neural tangent kernel regression

    Yingyu Liang, Zhizhou Sha, Zhenmei Shi, and Zhao Song. Differential privacy mechanisms in neural tangent kernel regression. arXiv preprint arXiv:2407.13621 , 2024

    2024 arXiv

  32. [40]

    Unraveling the smoothness properties of diffusion models: A gaussian mixture perspective

    Yingyu Liang, Zhenmei Shi, Zhao Song, and Yufa Zhou. Unraveling the smoothness properties of diffusion models: A gaussian mixture perspective. arXiv preprint arXiv:2405.16418 , 2024

    2024 arXiv

  33. [41]

    Score-based generative diffusion models for social recommendations

    Chengyi Liu, Jiahao Zhang, Shijie Wang, Wenqi Fan, and Qing Li. Score-based generative diffusion models for social recommendations. arXiv preprint arXiv:2412.15579 , 2024

    2024 arXiv

  34. [42]

    Conditional generative adversarial nets

    Mehdi Mirza and Simon Osindero. Conditional generative adversarial nets. In arXiv preprint arXiv:1411.1784 , 2014

    2014 arXiv

  35. [43]

    Memoire sur la theorie des deblais et des remblais

    Gaspard Monge. Memoire sur la theorie des deblais et des remblais . 1781

  36. [44]

    Pixel recurrent neural networks

    Aaron van den Oord, Nal Kalchbrenner, and Koray Kavukcuoglu. Pixel recurrent neural networks. In International conference on machine learning , pages 1747--1756, 2016

    2016

  37. [45]

    High-resolution image synthesis with latent diffusion models

    Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bj \"o rn Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 10684--10695, 2022

    2022

  38. [46]

    Deep unsupervised learning using nonequilibrium thermodynamics

    Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. In International conference on machine learning , pages 2256--2265. PMLR, 2015

    2015

  39. [47]

    Aligned diffusion schr \"o dinger bridges

    Vignesh Ram Somnath, Matteo Pariset, Ya-Ping Hsieh, Maria Rodriguez Martinez, Andreas Krause, and Charlotte Bunne. Aligned diffusion schr \"o dinger bridges. In Uncertainty in Artificial Intelligence , pages 1985--1995. PMLR, 2023

    1985

  40. [48]

    Score-based generative modeling through stochastic differential equations

    Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations (ICLR) , 2021

    2021

  41. [49]

    Lazydit: Lazy learning for the acceleration of diffusion transformers

    Xuan Shen, Zhao Song, Yufa Zhou, Bo Chen, Yanyu Li, Yifan Gong, Kai Zhang, Hao Tan, Jason Kuen, Henghui Ding, Zhihao Shu, Wei Niu, Pu Zhao, Yanzhi Wang, and Jiuxiang Gu. Lazydit: Lazy learning for the acceleration of diffusion transformers. In Proceedings of the AAAI Conferenc...

    2025

  42. [50]

    Rossi, Hao Tan, Tong Yu, Xiang Chen, Yufan Zhou, Tong Sun, Pu Zhao, Yanzhi Wang, and Jiuxiang Gu

    Xuan Shen, Zhao Song, Yufa Zhou, Bo Chen, Jing Liu, Ruiyi Zhang, Ryan A. Rossi, Hao Tan, Tong Yu, Xiang Chen, Yufan Zhou, Tong Sun, Pu Zhao, Yanzhi Wang, and Jiuxiang Gu. Numerical pruning for efficient autoregressive models. In Proceedings of the AAAI Conference on Artificial...

    2025

  43. [51]

    Visual autoregressive modeling: Scalable image generation via next-scale prediction

    Keyu Tian, Yi Jiang, Zehuan Yuan, Bingyue Peng, and Liwei Wang. Visual autoregressive modeling: Scalable image generation via next-scale prediction. Advances in neural information processing systems , 2024

    2024

  44. [52]

    Optimal transport: old and new

    Cedric Villani. Optimal transport: old and new . Springer, 2008

    2008

  45. [53]

    Attention is all you need

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, ukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information processing systems , pages 5998--6008, 2017

    2017

  46. [54]

    Modeling the trade-off of privacy preservation and activity recognition on low-resolution images

    Yuntao Wang, Zirui Cheng, Xin Yi, Yan Kong, Xueyang Wang, Xuhai Xu, Yukang Yan, Chun Yu, Shwetak Patel, and Yuanchun Shi. Modeling the trade-off of privacy preservation and activity recognition on low-resolution images. In Proceedings of the 2023 CHI Conference on Human Factor...

    2023

  47. [55]

    Dolfin: Diffusion layout transformers without autoencoder

    Yilin Wang, Zeyuan Chen, Liangjun Zhong, Zheng Ding, Zhizhou Sha, and Zhuowen Tu. Dolfin: Diffusion layout transformers without autoencoder. arXiv preprint arXiv:2310.16305 , 2023

    2023 arXiv

  48. [56]

    Omnicontrolnet: Dual-stage integration for conditional image generation

    Yilin Wang, Haiyang Xu, Xiang Zhang, Zeyuan Chen, Zhizhou Sha, Zirui Wang, and Zhuowen Tu. Omnicontrolnet: Dual-stage integration for conditional image generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 7436--7448, 2024

    2024

  49. [57]

    Bayesian diffusion models for 3d shape reconstruction

    Haiyang Xu, Yu Lei, Zeyuan Chen, Xiang Zhang, Yue Zhao, Yilin Wang, and Zhuowen Tu. Bayesian diffusion models for 3d shape reconstruction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 10628--10638, 2024

    2024

  50. [58]

    Perflow: Piecewise rectified flow as universal plug-and-play accelerator

    Hanshu Yan, Xingchao Liu, Jiachun Pan, Jun Hao Liew, Qiang Liu, and Jiashi Feng. Perflow: Piecewise rectified flow as universal plug-and-play accelerator. arXiv preprint arXiv:2405.07510 , 2024

    2024 arXiv

  51. [59]

    Uni-3d: A universal model for panoptic 3d scene reconstruction

    Xiang Zhang, Zeyuan Chen, Fangyin Wei, and Zhuowen Tu. Uni-3d: A universal model for panoptic 3d scene reconstruction. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pages 9256--9266, 2023

    2023

  52. [60]

    Improved techniques for maximum likelihood estimation for diffusion odes

    Kaiwen Zheng, Cheng Lu, Jianfei Chen, and Jun Zhu. Improved techniques for maximum likelihood estimation for diffusion odes. In International Conference on Machine Learning , pages 42363--42389. PMLR, 2023

    2023

  53. [61]

    Denoising diffusion bridge models

    Linqi Zhou, Aaron Lou, Samar Khanna, and Stefano Ermon. Denoising diffusion bridge models. arXiv preprint arXiv:2309.16948 , 2023

    2023 arXiv

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.