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REVIEW 3 major objections 6 minor 251 references

Trajectory inference via Acceleration Matching

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper proposes Acceleration Matching, a simulation-free regression algorithm that learns smooth phase-space dynamics matching prescribed marginals at every observation time.

desk verdict A clever simulation-free phase-space trajectory inference method with an explicit kinetic bridge drift, but the central theorem's Lipschitz hypothesis is unverified and fails for the atomic marginals it targets, leaving the exact-marginal guarantee unproven. read the letter →

arxiv 2608.03916 v1 pith:5JZ5C35L submitted 2026-08-04 cs.LG math.OCstat.ML

Bartolo Dazzini , Giovanni Conforti , Alain Durmus , Aram-Alexandre Pooladian This is my paper · ORCID
classification cs.LGmath.OCstat.ML
keywords trajectoryinferencekineticBrownianbridgephase-spacedynamicssimulation-freetrainingmulti-marginalconstraintsflowmatchingstochasticdifferentialequationssingle-cellRNAsequencing
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

Acceleration Matching (AM) is a proposed answer to a concrete problem: from unpaired position snapshots at several time points, produce smooth random trajectories whose position distribution at each snapshot time equals the observed one. The paper's central claim is that this can be done by picking the acceleration field of a second-order stochastic differential equation to be the conditional expectation of the explicit kinetic Brownian bridge acceleration. With that field, the non-Markovian interpolant and a Markov diffusion driven by the field have identical marginals at every time (Theorem 1), so a squared-residual regression against the explicit bridge acceleration is a valid, simulation-free training objective. The method needs only positional data, avoids trajectory simulation during training, and requires no smoothing preprocessing. The paper reports numerical evidence on ocean-current, predator-prey, and single-cell benchmarks indicating that AM matches or beats existing flow-matching and phase-space methods on held-out marginals.

What carries the argument

The load-bearing object is the kinetic Brownian bridge: kinetic (underdamped) Brownian motion $dX_t = V_t\,dt$, $dV_t = \sqrt{\varepsilon}\,dB_t$ conditioned to start and end at prescribed phase-space points. Doob's $h$-transform makes its drift explicit, equation (7), with inverse-square and inverse-time terms in the remaining time $t_{j+1}-t$. The paper's central mechanism is the Markovianization step: averaging this bridge drift over the future endpoint conditionally on the current position and velocity yields an acceleration field that depends only on the present state, and Theorem 1 shows the resulting diffusion and the original non-Markovian interpolant share the same marginals for all $t$. This is what converts trajectory inference into regression onto a known field.

What would settle it

Simulate the ideal Markovianized SDE for a single interval with known endpoints and compare its terminal marginal to the kinetic Brownian bridge terminal law as the Euler step shrinks; disagreement would disprove the marginal-matching mechanism. Separately, on a dataset where the distribution of initial velocity given position is clearly non-Gaussian, the learned Gaussian sampler should fail to satisfy held-out marginals if the practical pipeline is the actual claim.

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Extended reading notes

Core claim

The paper establishes, as a mathematical statement, that the multi-marginal trajectory interpolation problem can be solved by a single Markovian second-order SDE. Starting from a kinetic Brownian motion conditioned to pass through sampled phase-space knots, the bridge drift on each interval is explicit: $a^j_t(x,v;x_{j+1},v_{j+1}) = \frac{6(x_{j+1}-x)}{(t_{j+1}-t)^2} - \frac{2(v_{j+1}+2v)}{t_{j+1}-t}$. Replacing this future-dependent drift by its conditional expectation given the current phase-space point produces a Markov process that, under a Lipschitz assumption, has the same law at every time as the pinned interpolant; in particular the position marginals satisfy the prescribed constraints. Therefore the quadratic regression loss on the explicit field has the correct Markovianized field as its unique minimizer, and the paper presents this as the first-order principle behind the training algorithm.

Load-bearing premise

The proof assumes the averaged acceleration field is Lipschitz so the kinetic Fokker–Planck equation has a unique solution, and it assumes the exact initial phase-space law; the practical algorithm replaces both with learned approximations, and the paper does not show the averaged field is Lipschitz near the interval endpoints where the bridge drift diverges.

Editorial extensions

If this is right

  • In the population limit, the regression loss is exact: its unique minimizer is the field from Theorem 1, so training never needs to simulate trajectories or enforce smoothness with splines.
  • The learned dynamics are second-order, so generated position paths have continuous velocities and are smooth by construction, unlike piecewise flow-matching stitches.
  • Multi-marginal constraints at observation times are built into the interpolant, and uneven time points are handled by $\Delta_j$ weights in the loss.
  • Because velocities are sampled jointly given all position knots, the objective couples intervals rather than decomposing into independent segment-wise regressions.
  • If Theorem 1's Lipschitz hypothesis holds, the same field can be integrated at inference by any SDE solver, with initial velocities drawn from the learned conditional sampler.

Reading between the lines

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

  • An extension not pursued in the paper is to use a richer conditional initial-velocity sampler than the diagonal Gaussian; the theorem's exactness hinges on reproducing $\mathrm{Law}(V_0\mid X_0)$, so any failure of the Gaussian model should show up as a systematic marginal error.
  • The explicit bridge drift blows up like $(t_{j+1}-t)^{-2}$ near the right endpoint, so discretization error there is the most plausible numerical bottleneck; truncating or reparameterizing the interval near the end is a testable modification.
  • The same conditional-expectation construction should carry over to damped kinetic Brownian motion ($\gamma>0$), since the appendix derives the analogous bridge drift; if so, the method gains a free parameter for tuning trajectory roughness while keeping the same simulation-free loss.
  • Because the loss is a simple regression, applying the same acceleration-matching principle to other reference processes, or to manifolds with explicit bridge drifts, would transfer the simulation-free property to those settings.
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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 / 6 minor

Summary. The paper proposes Acceleration Matching (AM), a method for trajectory inference from unpaired marginal snapshots at discrete times. The method lifts the problem to phase space, constructs an interpolation process from kinetic Brownian bridges conditioned on positional knots drawn from a coupling of the marginals, and derives an explicit conditional acceleration field. The central theoretical result, Theorem 1, states that the Markovianized acceleration field obtained by conditional expectation of the bridge acceleration yields a diffusion with the same marginals as the interpolant, provided the field is Lipschitz. The training objective regresses a neural network onto this field using only positional data, avoiding trajectory simulation during training. Numerical experiments on low- and high-dimensional benchmarks compare AM with flow-matching baselines and show competitive or superior performance on several metrics.

Significance. If the theoretical guarantee were fully established, the paper would make a valuable contribution: an explicit, simulation-free, preprocessing-light objective for multi-marginal trajectory inference with smooth paths. The closed-form bridge acceleration in Lemma 2 and the held-out marginal evaluation are genuine strengths, and the experimental design avoids circularity by testing on out-of-sample time points. However, the main theorem's Lipschitz hypothesis is not verified for the constructed field and fails for discrete empirical marginals, which are exactly the setting of all experiments. The central guarantee is therefore currently unproven, and the practical algorithm replaces the exact field and initial law with learned approximations, so the paper's stated guarantees do not apply to the implemented method without further argument.

major comments (3)
  1. [Section 3.1, Theorem 1] The Lipschitz hypothesis on the Markovianized acceleration field a^M_t is not verified and fails for the paper's own construction in a two-marginal example. For J=1, ρ0=δ0, ρ1=δ1, and V0~N(0,σ_v^2 I), using the Gaussian conditioning of Lemma A.1 gives a^M_t(x,v)=3(1-x)/(1-t)^2 - 3v/(1-t). Its derivative with respect to x is -3/(1-t)^2, which diverges as t↑1, so a^M is not Lipschitz uniformly in t and the uniqueness hypothesis for the kinetic Fokker-Planck equation is not satisfied. Since all numerical experiments use empirical (atomic) marginals, this singular behavior is present in the exact interpolant for the data regime the paper targets. The proof of Theorem 1 therefore does not establish the claimed equality Law(X^M_t,V^M_t)=Law(X^I_t,V^I_t) or the marginal constraints (1) without an additional well-posedness argument for singular drifts.
  2. [Section 3.2, Algorithms 1 and 2] Even under the assumptions of Theorem 1, the implemented pipeline replaces the exact conditional expectation a^M_t with a learned network a_θ and the exact initial law P^I_0 with a learned Gaussian sampler q_ϕ. Consequently the statements in the Introduction and Section 3.1 that AM 'is guaranteed to satisfy the constraints (1)' do not apply to the trained model; they hold at most for the idealized regression target in the limit of perfect approximation. The paper should either qualify these claims explicitly or provide an approximation-error analysis showing how the learned quantities inherit the marginal-matching property.
  3. [Appendix A.3, proof of Theorem 1] The proof applies the tower property to E[a^j_t(X^I_t,V^I_t;X^I_{t_{j+1}},V^I_{t_{j+1}})|(X^I_t,V^I_t)] without establishing that the singular terms in (7), which grow like (t_{j+1}-t)^{-2} near the right endpoint, are integrable under the conditional law. This integrability is not automatic and needs a separate argument, especially when the marginals are atomic. This gap is separate from the Lipschitz issue but is likewise load-bearing for the derivation of the Markovianized field.
minor comments (6)
  1. [Section 1, paragraph 2] The phrase 'is guaranteed to satisfy the constraints (1)' overstates the result given the learned approximations described in Section 3.2; a more cautious wording is needed.
  2. [Section 4.1, Table 1] On the GoM dataset, the held-out W2 of AM (0.163±0.010) is larger than the reported 3MSBM value (0.135), so the summary sentence 'competitive with or superior to existing algorithms' should be nuanced to reflect this comparison.
  3. [Section 2.2, Equation (KFP)] The sentence 'the pair (µ^a_t, a_t) satisfies the kinetic Fokker-Planck equation' is imprecise; it is the measure-valued path t↦µ^a_t that satisfies the equation given the field a_t.
  4. [Algorithm 1, line 9] The displayed loss uses a single sampled time s_j per interval per minibatch; the paper does not state that this gives an unbiased estimator of the population loss (9), which would help clarify the stochastic optimization.
  5. [Appendix B.1] The number of paired samples (x^(i)_0, v^(i)_0) used to train the initial-velocity sampler q_ϕ is not reported; Table 10 gives hyperparameters but not the dataset size for this step.
  6. [References] The Tong et al. (2024) reference ends with 'Expert Certification.' which appears to be a BibTeX artifact rather than part of the title.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the acceleration field is an analytic Markovianization of an explicitly pinned reference process, not a fitted prediction; held-out marginals are out-of-sample.

full rationale

The central construction defines the interpolant P_I as kinetic Brownian motion conditioned on knots sampled from a coupling of the prescribed marginals, so the constraint (1) is an input. Theorem 1 then proves, via the tower property and uniqueness for the kinetic Fokker–Planck equation, that the Markovianized acceleration field a^M (the conditional expectation of the explicit bridge acceleration (7)) reproduces the law of P_I at every time. This is a genuine derivation rather than a renaming: the equality Law(X^M_t,V^M_t)=Law(X^I_t,V^I_t) does not follow from the definition of a^M alone, and the proof does not invoke any result from the authors' prior work. The regression loss (9) targets the explicit bridge acceleration; its minimizer being a^M is a standard conditional-expectation fact, and the learned a_theta and q_phi are approximations, not fitted 'predictions' of the held-out marginals. Held-out times (e.g., t1,t3,t5,t7 in GoM/LV) are not used in the coupling or loss and therefore provide a genuine out-of-sample test. The self-citations (Pooladian et al. 2023; Baptista et al. 2025; Conforti et al. 2025) are contextual or future-work and are not load-bearing. The paper's own admission that 3MSBM results could not be reproduced is a reproducibility limitation. The unverified Lipschitz hypothesis in Theorem 1 and the replacement of P^I_0 by q_phi are correctness/rigor gaps, not circularity: they concern whether the stated guarantee applies, not whether the derivation reduces to its inputs. No circular step can be exhibited by equation comparison, so no step is reported.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim depends on a small set of hand-set hyperparameters (sigma_v^2, epsilon) and on the Gaussian initial velocity assumption. The Lipschitz condition on a^M is stated but not proven. No new physical entities are introduced; the Markovianized acceleration field is a mathematical construction defined from the reference process.

free parameters (2)
  • sigma_v_squared = 50 (GoM), 50 (LV), 0.005 (EB5), 0.01 (CITE5), 1 (CITE50)
    Initial velocity variance in the assumed Gaussian law V0|X0 ~ N(0, sigma_v^2 I). Set per dataset in Table 11 with no described selection procedure; it directly shapes the bridge sampling and the learned initial velocity sampler.
  • epsilon = 16 (GoM), 4 (LV), 0.04 (EB5), 1e-4 (CITE5), 1e-4 (CITE50)
    Diffusion coefficient of the reference kinetic Brownian motion. Chosen per dataset in Table 11, it controls trajectory roughness and the conditional bridge formulas, and is not derived from first principles.
assumptions (5)
  • domain assumption The initial velocity conditional law is Gaussian: V0|X0 ~ N(0, sigma_v^2 I).
    Used in Lemma 1 to obtain explicit Gaussian conditioning formulas for V_t|X_t; this is a modeling choice that may not reflect true velocity distributions in the data.
  • ad hoc to paper The Markovianized acceleration field a^M is Lipschitz in (x,v) uniformly in t.
    Stated as a supposition in Theorem 1 without proof; the bridge drift (7) has (t_{j+1}-t)^{-2} singular terms, so Lipschitzness is not obvious and is load-bearing for well-posedness.
  • domain assumption The coupling pi across marginals is the independent (product) coupling.
    Section 3.1 says 'for simplicity, consider the independent coupling of the marginals'; this choice defines the interpolation measure P^I and thus the learned acceleration field, and is not varied or ablated in the experiments.
  • domain assumption The empirical measures are treated as the population distributions.
    Training and evaluation replace rho_tj with empirical measures; no finite-sample or generalization analysis is provided, so the method's guarantees hold only in the population limit.
  • standard math The reference SDE and the Markovianized SDE have unique weak solutions under the stated drift conditions.
    Standard Ito theory is invoked in the proof of Theorem 1 for Fokker-Planck uniqueness; the conditions on a^M are assumed rather than verified.

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Pith. "Pith review of Trajectory inference via Acceleration Matching." pith.science (2026). https://pith.science/paper/5JZ5C35L

@misc{pith2026260803916,
  author       = {Pith},
  title        = {Pith review of: Trajectory inference via Acceleration Matching},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5JZ5C35L}},
  note         = {Machine review of arXiv:2608.03916}
}
read the original abstract

Trajectory inference is a fundamental problem in many scientific domains: given a collection of unpaired snapshots of observations at discrete time points, the goal is to generate smooth trajectories that best resemble and interpolate the data. Existing algorithms exhibit computational challenges: they either rely on preprocessing subroutines to enforce smoothness or on simulation-based training objectives, both of which can be expensive. In order to overcome these limitations, we propose a new algorithm called Acceleration Matching (\texttt{AM}). Our approach consists of lifting the original interpolation problem to phase space and then regressing onto an explicit conditional acceleration field that induces random, smooth trajectories that agree with the prescribed marginals. Importantly, our resulting training algorithm only requires positional data, avoids trajectory simulation during training, and is devoid of expensive preprocessing. We provide ample numerical evidence suggesting that \texttt{AM} is competitive with or superior to existing algorithms on several benchmark problems from the existing literature.

Figures

Figures reproduced from arXiv: 2608.03916 by the authors.

Figure 1
Figure 1. AM outputs smoother trajectories (right) than piecewise flow matching (left). 2015; Kazakeviˇcius et al., 2021; Yeo et al., 2021; Bunne et al., 2022; Kubica et al., 2007; Liounis et al., 2020). In each of these cases, data are obtained over time in the form of unpaired observations. For example, the destructive nature of single-cell RNA sequencing makes it impossible to have repeated measurements of the same cell ov… view at source ↗
Figure 2
Figure 2. Visualization of trajectories generated for the GoM dataset. [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Visualization of trajectories generated for the LV dataset. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Visualization of generated marginals by AM and MMFMvan and MMFMconst on the EB5 dataset in the LOO setting (t1 is left out). they first compute pairwise optimal transport matchings between the marginals. For datasets of moderate size, these matchings can be obtained us…
Figure 5
Figure 5. Figure 5: Visualization of marginals generated by AM, MMFMvan, and MMFMconst for the first PCA com￾ponents on the CITE5 dataset in the LOO setting (t1 is left out) [PITH_FULL_IMAGE:figures/full_fig_p027_5.png]

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Works this paper leans on

251 extracted references · 61 canonical work pages

  1. [1]

    Goel, Narendra S and Maitra, Samaresh C and Montroll, Elliott W , journal=. On the. 1971 , publisher=

    1971

  2. [2]

    Trajectory Inference with Smooth

    Hong, Wanli and Shi, Yuliang and Niles-Weed, Jonathan , booktitle =. Trajectory Inference with Smooth. 2025 , volume =

    2025

  3. [3]

    The Annals of Applied Probability , volume=

    Toward a mathematical theory of trajectory inference , author=. The Annals of Applied Probability , volume=. 2024 , publisher=

    2024

  4. [4]

    An empirical

    Robbins, Herbert E , booktitle=. An empirical. 1992 , publisher=

    1992

  5. [5]

    Conditional simulation via entropic optimal transport:

    Baptista, Ricardo and Pooladian, Aram-Alexandre and Brennan, Michael and Marzouk, Youssef and Niles-Weed, Jonathan , booktitle =. Conditional simulation via entropic optimal transport:

  6. [6]

    2022 , publisher=

    Bogachev, Vladimir I and Krylov, Nicolai V and R. 2022 , publisher=

    2022

  7. [7]

    Icarus , volume=

    Efficient intra- and inter-night linking of asteroid detections using kd-trees , author=. Icarus , volume=. 2007 , publisher=

    2007

  8. [8]

    Earth and Space Science , volume=

    Autonomous detection of particles and tracks in optical images , author=. Earth and Space Science , volume=. 2020 , publisher=

    2020

Show all 251 references
  1. [9]

    Wiley Interdisciplinary Reviews: Climate Change , volume=

    Stochastic climate theory and modeling , author=. Wiley Interdisciplinary Reviews: Climate Change , volume=. 2015 , publisher=

    2015

  2. [10]

    Entropy , volume=

    Understanding the nature of the long-range memory phenomenon in socioeconomic systems , author=. Entropy , volume=. 2021 , publisher=

    2021

  3. [11]

    Nature communications , volume=

    Generative modeling of single-cell time series with PRESCIENT enables prediction of cell trajectories with interventions , author=. Nature communications , volume=. 2021 , publisher=

    2021

  4. [12]

    International Conference on Artificial Intelligence and Statistics , pages=

    Proximal optimal transport modeling of population dynamics , author=. International Conference on Artificial Intelligence and Statistics , pages=. 2022 , organization=

    2022

  5. [13]

    arXiv preprint arXiv:2508.04351 , year=

    Multi-marginal stochastic flow matching for high-dimensional snapshot data at irregular time points , author=. arXiv preprint arXiv:2508.04351 , year=

    arXiv

  6. [14]

    Deep momentum multi-marginal

    Chen, Tianrong and Liu, Guan-Horng and Tao, Molei and Theodorou, Evangelos , journal=. Deep momentum multi-marginal

  7. [15]

    Multi-marginal

    Shen, Yunyi and Berlinghieri, Renato and Broderick, Tamara , journal=. Multi-marginal

  8. [16]

    Tree-based diffusion

    Noble, Maxence and De Bortoli, Valentin and Doucet, Arnaud and Durmus, Alain , journal=. Tree-based diffusion

  9. [17]

    and De Bortoli, Valentin and Mathieu, Emile and Doucet, Arnaud and Barzilay, Regina and Jaakkola, Tommi , booktitle =

    Yim, Jason and Trippe, Brian L. and De Bortoli, Valentin and Mathieu, Emile and Doucet, Arnaud and Barzilay, Regina and Jaakkola, Tommi , booktitle =. 2023 , month =

    2023

  10. [18]

    Nichol, Alex and Dhariwal, Prafulla and Ramesh, Aditya and Shyam, Pranav and Mishkin, Pamela and McGrew, Bob and Sutskever, Ilya and Chen, Mark , journal=

  11. [19]

    arXiv preprint arXiv:2302.03660 , year=

    Flow matching on general geometries , author=. arXiv preprint arXiv:2302.03660 , year=

    arXiv

  12. [20]

    Haviv, Doron and Pooladian, Aram-Alexandre and Pe'Er, Dana and Amos, Brandon , booktitle =

  13. [21]

    2025 , publisher=

    Conforti, Giovanni and Durmus, Alain and Silveri, Marta Gentiloni , journal=. 2025 , publisher=

    2025

  14. [22]

    Transactions on Machine Learning Research , issn=

    Improving and generalizing flow-based generative models with minibatch optimal transport , author=. Transactions on Machine Learning Research , issn=. 2024 , url=

    2024

  15. [23]

    Proceedings of the 40th International Conference on Machine Learning , year =

    Multisample Flow Matching: Straightening Flows with Minibatch Couplings , author =. Proceedings of the 40th International Conference on Machine Learning , year =

  16. [24]

    Fast and smooth interpolation on

    Chewi, Sinho and Clancy, Julien and Le Gouic, Thibaut and Rigollet, Philippe and Stepaniants, George and Stromme, Austin , booktitle=. Fast and smooth interpolation on. 2021 , organization=

    2021

  17. [25]

    Second-order models for optimal transport and cubic splines on the

    Benamou, Jean-David and Gallou. Second-order models for optimal transport and cubic splines on the. Foundations of Computational Mathematics , volume=. 2019 , publisher=

    2019

  18. [26]

    arXiv preprint arXiv:2310.03725 , year=

    Stochastic interpolants with data-dependent couplings , author=. arXiv preprint arXiv:2310.03725 , year=

    arXiv

  19. [27]

    Go with the flow:

    Rapakoulias, George and Pedram, Ali Reza and Liu, Fengjiao and Zhu, Lingjiong and Tsiotras, Panagiotis , journal=. Go with the flow:

  20. [28]

    Entropic turnpike estimates for the kinetic

    Chiarini, Alberto and Conforti, Giovanni and Greco, Giacomo and Ren, Zhenjie , journal=. Entropic turnpike estimates for the kinetic. 2022 , publisher=

    2022

  21. [29]

    Mathematical tables and other aids to computation , volume=

    A smoothest curve approximation , author=. Mathematical tables and other aids to computation , volume=. 1957 , publisher=

    1957

  22. [30]

    arXiv preprint arXiv:2602.09639 , year=

    Blind denoising diffusion models and the blessings of dimensionality , author=. arXiv preprint arXiv:2602.09639 , year=

    arXiv

  23. [31]

    Stochastic interpolants:

    Albergo, Michael and Boffi, Nicholas M and Vanden-Eijnden, Eric , journal=. Stochastic interpolants:

  24. [32]

    ESAIM: Mathematical Modelling and Numerical Analysis , volume=

    Multi-marginal optimal transport: theory and applications , author=. ESAIM: Mathematical Modelling and Numerical Analysis , volume=. 2015 , publisher=

    2015

  25. [33]

    The Thirteenth International Conference on Learning Representations , year=

    Modeling complex system dynamics with flow matching across time and conditions , author=. The Thirteenth International Conference on Learning Representations , year=

  26. [34]

    Kinetic Optimal Transport (

    Brigati, Giovanni and Maas, Jan and Quattrocchi, Filippo , journal=. Kinetic Optimal Transport (

  27. [35]

    Measure-valued spline curves:

    Chen, Yongxin and Conforti, Giovanni and Georgiou, Tryphon T , journal=. Measure-valued spline curves:. 2018 , publisher=

    2018

  28. [36]

    Momentum Multi-Marginal

    Theodoropoulos, Panagiotis and Saravanos, Augustinos and Theodorou, Evangelos and Liu, Guan-Horng , booktitle =. Momentum Multi-Marginal

  29. [37]

    Statistical optimal transport , url =

    Sinho Chewi and Jonathan Niles-Weed and Philippe Rigollet , date-added =. Statistical optimal transport , url =. 2024 , bdsk-url-1 =. 2407.18163 , month =

    2024 arXiv

  30. [38]

    arXiv preprint arXiv:2310.02557 , title =

    Kadkhodaie, Zahra and Guth, Florentin and Simoncelli, Eero P and Mallat, St. arXiv preprint arXiv:2310.02557 , title =

    arXiv

  31. [39]

    Sampling from a

    Stromme, Austin , booktitle =. Sampling from a

  32. [40]

    On the relation between optimal transport and

    Chen, Yongxin and Georgiou, Tryphon T and Pavon, Michele , journal =. On the relation between optimal transport and

  33. [41]

    Trajectory inference via mean-field

    Chizat, L. Trajectory inference via mean-field. Advances in Neural Information Processing Systems , pages =

  34. [42]

    Towards a mathematical theory of trajectory inference , year =

    Lavenant, Hugo and Zhang, Stephen and Kim, Young-Heon and Schiebinger, Geoffrey , journal =. Towards a mathematical theory of trajectory inference , year =

  35. [43]

    Video diffusion models , volume =

    Ho, Jonathan and Salimans, Tim and Gritsenko, Alexey and Chan, William and Norouzi, Mohammad and Fleet, David J , journal =. Video diffusion models , volume =

  36. [44]

    Audiobox: Unified audio generation with natural language prompts , year =

    Vyas, Apoorv and Shi, Bowen and Le, Matthew and Tjandra, Andros and Wu, Yi-Chiao and Guo, Baishan and Zhang, Jiemin and Zhang, Xinyue and Adkins, Robert and Ngan, William and others , journal =. Audiobox: Unified audio generation with natural language prompts , year =

  37. [45]

    Score-based generative neural networks for large-scale optimal transport , volume =

    Daniels, Max and Maunu, Tyler and Hand, Paul , journal =. Score-based generative neural networks for large-scale optimal transport , volume =

  38. [46]

    Optimized Linear Measurements for Inverse Problems using Diffusion-Based Image Generation , year =

    Zhang, Ling-Qi and Kadkhodaie, Zahra and Simoncelli, Eero P and Brainard, David H , journal =. Optimized Linear Measurements for Inverse Problems using Diffusion-Based Image Generation , year =

  39. [47]

    Diffusion models:

    Yang, Ling and Zhang, Zhilong and Song, Yang and Hong, Shenda and Xu, Runsheng and Zhao, Yue and Zhang, Wentao and Cui, Bin and Yang, Ming-Hsuan , journal =. Diffusion models:

  40. [48]

    Score-based generative modeling through stochastic differential equations , year =

    Song, Yang and Sohl-Dickstein, Jascha and Kingma, Diederik P and Kumar, Abhishek and Ermon, Stefano and Poole, Ben , journal =. Score-based generative modeling through stochastic differential equations , year =

  41. [49]

    Deep unsupervised learning using nonequilibrium thermodynamics , year =

    Sohl-Dickstein, Jascha and Weiss, Eric and Maheswaranathan, Niru and Ganguli, Surya , booktitle =. Deep unsupervised learning using nonequilibrium thermodynamics , year =

  42. [50]

    Fortet, Robert , journal =. R

  43. [51]

    Convergence of score-based generative modeling for general data distributions , year =

    Lee, Holden and Lu, Jianfeng and Tan, Yixin , booktitle =. Convergence of score-based generative modeling for general data distributions , year =

  44. [52]

    Diffusion models are minimax optimal distribution estimators , year =

    Oko, Kazusato and Akiyama, Shunta and Suzuki, Taiji , booktitle =. Diffusion models are minimax optimal distribution estimators , year =

  45. [53]

    Optimal score estimation via empirical

    Wibisono, Andre and Wu, Yihong and Yang, Kaylee Yingxi , journal =. Optimal score estimation via empirical

  46. [54]

    arXiv preprint arXiv:2310.12395 , title =

    Scarvelis, Christopher and Borde, Haitz S. arXiv preprint arXiv:2310.12395 , title =

    arXiv

  47. [55]

    Brownian motion, martingales, and stochastic calculus , year =

    Le Gall, Jean-Fran. Brownian motion, martingales, and stochastic calculus , year =

  48. [56]

    Stochastic control liaisons:

    Chen, Yongxin and Georgiou, Tryphon T and Pavon, Michele , journal =. Stochastic control liaisons:

  49. [57]

    Diffusion

    Shi, Yuyang and De Bortoli, Valentin and Campbell, Andrew and Doucet, Arnaud , journal =. Diffusion

  50. [58]

    Conditional simulation using diffusion

    Shi, Yuyang and De Bortoli, Valentin and Deligiannidis, George and Doucet, Arnaud , booktitle =. Conditional simulation using diffusion

  51. [59]

    Bunne, Charlotte and Hsieh, Ya-Ping and Cuturi, Marco and Krause, Andreas , booktitle =. The

  52. [60]

    Probabilistic Forecasting with Stochastic Interpolants and

    Chen, Yifan and Goldstein, Mark and Hua, Mengjian and Albergo, Michael S and Boffi, Nicholas M and Vanden-Eijnden, Eric , journal =. Probabilistic Forecasting with Stochastic Interpolants and

  53. [61]

    One-step data-driven generative model via

    Huang, Hanwen , journal =. One-step data-driven generative model via

  54. [62]

    Sampling via

    Ding, Zhao and Jiao, Yuling and Lu, Xiliang and Yang, Zhijian and Yuan, Cheng , journal =. Sampling via

  55. [63]

    A computational fluid mechanics solution to the

    Benamou, Jean-David and Brenier, Yann , journal =. A computational fluid mechanics solution to the

  56. [64]

    Large deviations for dynamical

    Kato, Kengo , journal =. Large deviations for dynamical

  57. [65]

    , date-modified =

    Tsybakov, Alexandre B. , date-modified =. Introduction to nonparametric estimation , url =. 2009 , bdsk-url-1 =. doi:10.1007/b13794 , isbn =

    2009 doi

  58. [66]

    Bayesian learning via neural

    Vargas, Francisco and Ovsianas, Andrius and Fernandes, David and Girolami, Mark and Lawrence, Neil D and N. Bayesian learning via neural. Statistics and Computing , number =

  59. [67]

    Huang, Jian and Jiao, Yuling and Kang, Lican and Liao, Xu and Liu, Jin and Liu, Yanyan , journal =. Schr

  60. [68]

    The probability flow

    Chen, Sitan and Chewi, Sinho and Lee, Holden and Li, Yuanzhi and Lu, Jianfeng and Salim, Adil , journal =. The probability flow

  61. [69]

    The Data-Driven

    Pavon, Michele and Trigila, Giulio and Tabak, Esteban G , journal =. The Data-Driven

  62. [70]

    Bernton, Espen and Heng, Jeremy and Doucet, Arnaud and Jacob, Pierre E , journal =. Schr

  63. [71]

    Lower complexity adaptation for empirical entropic optimal transport , year =

    Groppe, Michel and Hundrieser, Shayan , journal =. Lower complexity adaptation for empirical entropic optimal transport , year =

  64. [72]

    Tight stability bounds for entropic

    Divol, Vincent and Niles-Weed, Jonathan and Pooladian, Aram-Alexandre , journal =. Tight stability bounds for entropic

  65. [73]

    arXiv preprint arXiv:1308.0215 , title =

    L. arXiv preprint arXiv:1308.0215 , title =

    arXiv

  66. [74]

    The Eleventh International Conference on Learning Representations , year=

    Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions , author=. The Eleventh International Conference on Learning Representations , year=

  67. [75]

    A relationship between arbitrary positive matrices and doubly stochastic matrices , volume =

    Sinkhorn, Richard , journal =. A relationship between arbitrary positive matrices and doubly stochastic matrices , volume =

  68. [76]

    Learning normalizing flows from

    Finlay, Chris and Gerolin, Augusto and Oberman, Adam M and Pooladian, Aram-Alexandre , journal =. Learning normalizing flows from

  69. [77]

    Convexity and regularity properties for entropic interpolations , volume =

    Ripani, Luigia , journal =. Convexity and regularity properties for entropic interpolations , volume =

  70. [78]

    Entropy-regularized 2-

    Mallasto, Anton and Gerolin, Augusto and Minh, H. Entropy-regularized 2-. Information Geometry , number =

  71. [79]

    arXiv preprint arXiv:2110.08084 , title =

    Bach, Francis and Chizat, Lena. arXiv preprint arXiv:2110.08084 , title =

    arXiv

  72. [80]

    Sparse optimization on measures with over-parameterized gradient descent , volume =

    Chizat, Lenaic , journal =. Sparse optimization on measures with over-parameterized gradient descent , volume =

  73. [81]

    Learning generative models with

    Genevay, Aude and Peyr. Learning generative models with. International Conference on Artificial Intelligence and Statistics , organization =

  74. [82]

    Sample complexity of

    Genevay, Aude and Chizat, L. Sample complexity of. The 22nd international conference on artificial intelligence and statistics , organization =

  75. [83]

    Statistical inference with regularized optimal transport , year =

    Goldfeld, Ziv and Kato, Kengo and Rioux, Gabriel and Sadhu, Ritwik , journal =. Statistical inference with regularized optimal transport , year =

  76. [84]

    Minimum intrinsic dimension scaling for entropic optimal transport , year =

    Stromme, Austin J , journal =. Minimum intrinsic dimension scaling for entropic optimal transport , year =

  77. [85]

    Quantitative stability of optimal transport maps and linearization of the 2-

    M. Quantitative stability of optimal transport maps and linearization of the 2-. International Conference on Artificial Intelligence and Statistics , organization =

  78. [86]

    Duke Mathematical Journal , title =

    Delalande, Alex and M. Duke Mathematical Journal , title =

  79. [87]

    Convergence rates for discretized

    Berman, Robert J , journal =. Convergence rates for discretized

  80. [88]

    Gigli, Nicola , journal =. On

  81. [89]

    The Annals of Statistics , volume=

    Plugin estimation of smooth optimal transport maps , author=. The Annals of Statistics , volume=. 2024 , publisher=

    2024

  82. [90]

    Optimal transport: old and new , volume =

    Villani, C. Optimal transport: old and new , volume =

  83. [91]

    Optimal transport for applied mathematicians , volume =

    Santambrogio, Filippo , journal =. Optimal transport for applied mathematicians , volume =

  84. [92]

    A Hamilton--Jacobi-based proximal operator , volume =

    Osher, Stanley and Heaton, Howard and Wu Fung, Samy , journal =. A Hamilton--Jacobi-based proximal operator , volume =

  85. [93]

    Minimax estimation of discontinuous optimal transport maps: The semi-discrete case , year =

    Pooladian, Aram-Alexandre and Divol, Vincent and Niles-Weed, Jonathan , journal =. Minimax estimation of discontinuous optimal transport maps: The semi-discrete case , year =

  86. [94]

    An entropic interpolation proof of the

    Gentil, Ivan and L. An entropic interpolation proof of the. Stochastic Processes and their Applications , number =

  87. [95]

    An optimal transport approach for the Schr

    Marino, Simone Di and Gerolin, Augusto , journal =. An optimal transport approach for the Schr

  88. [96]

    An entropic generalization of

    Chewi, Sinho and Pooladian, Aram-Alexandre , journal =. An entropic generalization of

  89. [97]

    arXiv preprint arXiv:2112.07275 , title =

    Vacher, Adrien and Vialard, Fran. arXiv preprint arXiv:2112.07275 , title =

    arXiv

  90. [98]

    International Conference on Learning Representations , title =

    Seguy, Vivien and Damodaran, Bharath Bhushan and Flamary, R. International Conference on Learning Representations , title =

  91. [99]

    Chizat, Lenaic and Roussillon, Pierre and L. Faster. Advances in Neural Information Processing Systems , pages =

  92. [100]

    Stochastic dynamics and the

    Bauerschmidt, Roland and Bodineau, Thierry and Dagallier, Benoit , journal =. Stochastic dynamics and the

  93. [101]

    Snowflake universality of

    Andoni, Alexandr and Naor, Assaf and Neiman, Ofer , journal =. Snowflake universality of

  94. [102]

    Spectral independence in high-dimensional expanders and applications to the hardcore model , year =

    Anari, Nima and Liu, Kuikui and Gharan, Shayan Oveis , journal =. Spectral independence in high-dimensional expanders and applications to the hardcore model , year =

  95. [103]

    Measure Theory , volume =

    Bogachev, Vladimir I , publisher =. Measure Theory , volume =

  96. [104]

    Entropic independence I: Modified log-

    Anari, Nima and Jain, Vishesh and Koehler, Frederic and Pham, Huy Tuan and Vuong, Thuy-Duong , journal =. Entropic independence I: Modified log-

  97. [105]

    High-resolution image synthesis with latent diffusion models , year =

    Rombach, Robin and Blattmann, Andreas and Lorenz, Dominik and Esser, Patrick and Ommer, Bj. High-resolution image synthesis with latent diffusion models , year =. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages =

  98. [106]

    Flow straight and fast:

    Liu, Xingchao and Gong, Chengyue and Liu, Qiang , journal =. Flow straight and fast:

  99. [107]

    Building normalizing flows with stochastic interpolants , year =

    Albergo, Michael S and Vanden-Eijnden, Eric , journal =. Building normalizing flows with stochastic interpolants , year =

  100. [108]

    Flow matching for generative modeling , year =

    Lipman, Yaron and Chen, Ricky TQ and Ben-Hamu, Heli and Nickel, Maximilian and Le, Matt , journal =. Flow matching for generative modeling , year =

  101. [109]

    Neural ordinary differential equations , volume =

    Chen, Ricky TQ and Rubanova, Yulia and Bettencourt, Jesse and Duvenaud, David K , journal =. Neural ordinary differential equations , volume =

  102. [110]

    Monge, Gaspard , journal =. M

  103. [111]

    Lee, Danyeong and Lee, Dohoon and Bang, Dongmin and Kim, Sun , booktitle =. Disco:

  104. [112]

    Sur la th

    Schr. Sur la th. Annales de l'institut Henri Poincar

  105. [113]

    Entropic optimal transport:

    Nutz, Marcel and Wiesel, Johannes , journal =. Entropic optimal transport:

  106. [114]

    Riemannian diffusion

    Thornton, James and Hutchinson, Michael and Mathieu, Emile and De Bortoli, Valentin and Teh, Yee Whye and Doucet, Arnaud , journal =. Riemannian diffusion

  107. [115]

    Quantifying brain state transition cost via

    Kawakita, Genji and Kamiya, Shunsuke and Sasai, Shuntaro and Kitazono, Jun and Oizumi, Masafumi , journal =. Quantifying brain state transition cost via

  108. [116]

    An extension of

    Bures, Donald , journal =. An extension of

  109. [117]

    A convexity principle for interacting gases , volume =

    McCann, Robert J , journal =. A convexity principle for interacting gases , volume =

  110. [118]

    Zero-shot text-to-image generation , year =

    Ramesh, Aditya and Pavlov, Mikhail and Goh, Gabriel and Gray, Scott and Voss, Chelsea and Radford, Alec and Chen, Mark and Sutskever, Ilya , booktitle =. Zero-shot text-to-image generation , year =

  111. [119]

    Likelihood training of

    Chen, Tianrong and Liu, Guan-Horng and Theodorou, Evangelos A , journal =. Likelihood training of

  112. [120]

    Energy-guided entropic neural optimal transport , year =

    Mokrov, Petr and Korotin, Alexander and Kolesov, Alexander and Gushchin, Nikita and Burnaev, Evgeny , journal =. Energy-guided entropic neural optimal transport , year =

  113. [121]

    Vargas, Francisco and Thodoroff, Pierre and Lamacraft, Austen and Lawrence, Neil , journal =. Solving

  114. [122]

    Progressive Entropic Optimal Transport Solvers , year =

    Kassraie, Parnian and Pooladian, Aram-Alexandre and Klein, Michal and Thornton, James and Niles-Weed, Jonathan and Cuturi, Marco , journal =. Progressive Entropic Optimal Transport Solvers , year =

  115. [123]

    Deep generalized

    Liu, Guan-Horng and Chen, Tianrong and So, Oswin and Theodorou, Evangelos , journal =. Deep generalized

  116. [124]

    Bayesian learning via neural

    Nusken, Nikolas and Vargas, Francisco and Ovsianas, Andrius and Fernandes, David and Girolami, Mark and Lawrence, Neil , journal =. Bayesian learning via neural

  117. [125]

    Light and Optimal

    Gushchin, Nikita and Kholkin, Sergei and Burnaev, Evgeny and Korotin, Alexander , booktitle =. Light and Optimal

  118. [126]

    Building the bridge of

    Gushchin, Nikita and Kolesov, Alexander and Mokrov, Petr and Karpikova, Polina and Spiridonov, Andrei and Burnaev, Evgeny and Korotin, Alexander , journal =. Building the bridge of

  119. [127]

    Mikulincer, Dan and Shenfeld, Yair , journal =. The

  120. [128]

    Rapid convergence of the unadjusted langevin algorithm: Isoperimetry suffices , volume =

    Vempala, Santosh and Wibisono, Andre , journal =. Rapid convergence of the unadjusted langevin algorithm: Isoperimetry suffices , volume =

  121. [129]

    Background modeling for double

    Manole, Tudor and Bryant, Patrick and Alison, John and Kuusela, Mikael and Wasserman, Larry , journal =. Background modeling for double

  122. [130]

    Eldan, Ronen and Lehec, Joseph and Shenfeld, Yair , title =

  123. [131]

    Learning generative models with

    Aude Genevay and Gabriel Peyr. Learning generative models with. Proceedings of the 21st International Conference on Artificial Intelligence and Statistics , pages =

  124. [132]

    Convergence of entropic schemes for optimal transport and gradient flows , volume =

    Carlier, Guillaume and Duval, Vincent and Peyr. Convergence of entropic schemes for optimal transport and gradient flows , volume =. SIAM Journal on Mathematical Analysis , number =

  125. [133]

    A formula for the time derivative of the entropic cost and applications , volume =

    Conforti, Giovanni and Tamanini, Luca , journal =. A formula for the time derivative of the entropic cost and applications , volume =

  126. [134]

    Entropy-regularized 2-Wasserstein distance between Gaussian measures , year =

    Mallasto, Anton and Gerolin, Augusto and Minh, H. Entropy-regularized 2-Wasserstein distance between Gaussian measures , year =. Information Geometry , pages =

  127. [135]

    Nearly tight convergence bounds for semi-discrete entropic optimal transport , year =

    Delalande, Alex , booktitle =. Nearly tight convergence bounds for semi-discrete entropic optimal transport , year =

  128. [136]

    Quantitative stability in the geometry of semi-discrete optimal transport , volume =

    Bansil, Mohit and Kitagawa, Jun , journal =. Quantitative stability in the geometry of semi-discrete optimal transport , volume =

  129. [137]

    arXiv , author =:2210.00225 , primaryclass =

    Displacement smoothness of entropic optimal transport , year =. arXiv , author =:2210.00225 , primaryclass =

    arXiv

  130. [138]

    Polar factorization and monotone rearrangement of vector-valued functions , volume =

    Brenier, Yann , fjournal =. Polar factorization and monotone rearrangement of vector-valued functions , volume =. Comm. Pure Appl. Math. , number =

  131. [139]

    Learning Generative Models with

    Aude Genevay and Gabriel Peyr. Learning Generative Models with. International Conference on Artificial Intelligence and Statistics,

  132. [140]

    Entropy-regularized optimal transport for machine learning , year =

    Genevay, Aude , school =. Entropy-regularized optimal transport for machine learning , year =

  133. [141]

    Computational optimal transport , volume =

    Peyr. Computational optimal transport , volume =. Foundations and Trends

  134. [142]

    Probability in high dimension , year =

    Van Handel, Ramon , institution =. Probability in high dimension , year =

  135. [143]

    Non-asymptotic convergence bounds for

    Greco, Giacomo and Noble, Maxence and Conforti, Giovanni and Durmus, Alain , booktitle =. Non-asymptotic convergence bounds for

  136. [144]

    Quantitative contraction rates for

    Conforti, Giovanni and Durmus, Alain and Greco, Giacomo , journal =. Quantitative contraction rates for

  137. [145]

    On the difference between entropic cost and the optimal transport cost , volume =

    Pal, Soumik , journal =. On the difference between entropic cost and the optimal transport cost , volume =

  138. [146]

    Stability of

    Nutz, Marcel and Wiesel, Johannes , journal =. Stability of

  139. [147]

    Capacity constrained entropic optimal transport,

    Benamou, Jean-David and Martinet, M. Capacity constrained entropic optimal transport,

  140. [148]

    arXiv preprint arXiv:2306.11895 , title =

    Klein, Michal and Pooladian, Aram-Alexandre and Ablin, Pierre and Ndiaye, Eug. arXiv preprint arXiv:2306.11895 , title =

    arXiv

  141. [149]

    , date-added =

    Kantorovitch, L. , date-added =. On the translocation of masses , volume =. C. R. (Doklady) Acad. Sci. URSS (N.S.) , mrclass =

  142. [150]

    Csisz\'. Ann. Probability , pages =

  143. [151]

    Near-linear time approximation algorithms for optimal transport via

    Jason Altschuler and Jonathan Weed and Philippe Rigollet , booktitle =. Near-linear time approximation algorithms for optimal transport via

  144. [152]

    Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance , volume =

    Weed, Jonathan and Bach, Francis , journal =. Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance , volume =

  145. [153]

    Monotonicity properties of optimal transportation and the

    Caffarelli, Luis A , journal =. Monotonicity properties of optimal transportation and the

  146. [154]

    Optimal transport tools (ott): A jax toolbox for all things wasserstein , year =

    Cuturi, Marco and Meng-Papaxanthos, Laetitia and Tian, Yingtao and Bunne, Charlotte and Davis, Geoff and Teboul, Olivier , journal =. Optimal transport tools (ott): A jax toolbox for all things wasserstein , year =

  147. [155]

    Journal of Machine Learning Research , number =

    R. Journal of Machine Learning Research , number =. 2021 , bdsk-url-1 =

    2021

  148. [156]

    Multivariate rank via entropic optimal transport: sample efficiency and generative modeling , year =

    Masud, Shoaib Bin and Werenski, Matthew and Murphy, James M and Aeron, Shuchin , journal =. Multivariate rank via entropic optimal transport: sample efficiency and generative modeling , year =

  149. [157]

    Bobkov, S. G. and G\". Exponential integrability and transportation cost related to logarithmic. J. Funct. Anal. , mrclass =. 1999 , bdsk-url-1 =. doi:10.1006/jfan.1998.3326 , fjournal =

    1999

  150. [158]

    Concentration inequalities , year =

    Boucheron, St\'. Concentration inequalities , year =. doi:10.1093/acprof:oso/9780199535255.001.0001 , isbn =

  151. [159]

    arXiv preprint arXiv:2202.06380 , title =

    del Barrio, Eustasio and Gonz. arXiv preprint arXiv:2202.06380 , title =

    arXiv

  152. [160]

    Central limit theorems for empirical transportation cost in general dimension , volume =

    del Barrio, Eustasio and Loubes, Jean-Michel , date-added =. Central limit theorems for empirical transportation cost in general dimension , volume =. Ann. Probab. , mrclass =. 2019 , bdsk-url-1 =. doi:10.1214/18-AOP1275 , fjournal =

    2019 doi

  153. [161]

    Statistical optimal transport via factored couplings , year =

    Forrow, Aden and H. Statistical optimal transport via factored couplings , year =. The 22nd International Conference on Artificial Intelligence and Statistics , date-added =

  154. [162]

    Multivariate ranks and quantiles using optimal transport: consistency, rates and nonparametric testing , volume =

    Ghosal, Promit and Sen, Bodhisattva , date-added =. Multivariate ranks and quantiles using optimal transport: consistency, rates and nonparametric testing , volume =. Ann. Statist. , mrclass =. 2022 , bdsk-url-1 =. doi:10.1214/21-aos2136 , fjournal =

    2022 doi

  155. [163]

    Mathematical foundations of infinite-dimensional statistical models , year =

    Gin. Mathematical foundations of infinite-dimensional statistical models , year =

  156. [164]

    On choosing and bounding probability metrics , volume =

    Gibbs, Alison L and Su, Francis Edward , journal =. On choosing and bounding probability metrics , volume =

  157. [165]

    Minkowski-type theorems and least-squares clustering , volume =

    Aurenhammer, Franz and Hoffmann, Friedrich and Aronov, Boris , journal =. Minkowski-type theorems and least-squares clustering , volume =

  158. [166]

    DALL.E-2 , year =

    OpenAI , howpublished =. DALL.E-2 , year =

  159. [167]

    Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , title =

    Robin Rombach and Andreas Blattmann and Dominik Lorenz and Patrick Esser and Bj. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , title =. 2022 , bdsk-url-1 =

    2022

  160. [168]

    Weak limits of entropy regularized Optimal Transport; potentials, plans and divergences , year =

    Gonzalez-Sanz, Alberto and Loubes, Jean-Michel and Niles-Weed, Jonathan , journal =. Weak limits of entropy regularized Optimal Transport; potentials, plans and divergences , year =

  161. [169]

    An improved central limit theorem and fast convergence rates for entropic transportation costs , year =

    del Barrio, Eustasio and Gonzalez-Sanz, Alberto and Loubes, Jean-Michel and Niles-Weed, Jonathan , journal =. An improved central limit theorem and fast convergence rates for entropic transportation costs , year =

  162. [170]

    Cuturi, Marco , journal =

  163. [171]

    Sharp convergence rates for empirical optimal transport with smooth costs , year =

    Manole, Tudor and Niles-Weed, Jonathan , journal =. Sharp convergence rates for empirical optimal transport with smooth costs , year =

  164. [172]

    On the difference between entropic cost and the optimal transport cost , year =

    Pal, Soumik , journal =. On the difference between entropic cost and the optimal transport cost , year =

  165. [173]

    From the

    L. From the. Journal of Functional Analysis , number =

  166. [174]

    Rates of estimation of optimal transport maps using plug-in estimators via barycentric projections , volume =

    Deb, Nabarun and Ghosal, Promit and Sen, Bodhisattva , journal =. Rates of estimation of optimal transport maps using plug-in estimators via barycentric projections , volume =

  167. [175]

    Minimax estimation of smooth optimal transport maps , volume =

    H. Minimax estimation of smooth optimal transport maps , volume =. The Annals of Statistics , number =

  168. [176]

    Entropic estimation of optimal transport maps , year =

    Pooladian, Aram-Alexandre and Niles-Weed, Jonathan , journal =. Entropic estimation of optimal transport maps , year =

  169. [177]

    Debiaser Beware: Pitfalls of Centering Regularized Transport Maps , year =

    Pooladian, Aram-Alexandre and Cuturi, Marco and Niles-Weed, Jonathan , journal =. Debiaser Beware: Pitfalls of Centering Regularized Transport Maps , year =

  170. [178]

    arXiv preprint arXiv:2112.01907 , title =

    Muzellec, Boris and Vacher, Adrien and Bach, Francis and Vialard, Fran. arXiv preprint arXiv:2112.01907 , title =

    arXiv

  171. [179]

    arXiv preprint arXiv:2203.09143 , title =

    Vacher, Adrien and Vialard, Fran. arXiv preprint arXiv:2203.09143 , title =

    arXiv

  172. [180]

    Optimal transport map estimation in general function spaces , year =

    Divol, Vincent and Niles-Weed, Jonathan and Pooladian, Aram-Alexandre , journal =. Optimal transport map estimation in general function spaces , year =

  173. [181]

    Convergence rates for regularized optimal transport via quantization , year =

    Eckstein, Stephan and Nutz, Marcel , journal =. Convergence rates for regularized optimal transport via quantization , year =

  174. [182]

    Entropic optimal transport: Geometry and large deviations , volume =

    Bernton, Espen and Ghosal, Promit and Nutz, Marcel , journal =. Entropic optimal transport: Geometry and large deviations , volume =

  175. [183]

    Stability of entropic optimal transport and

    Ghosal, Promit and Nutz, Marcel and Bernton, Espen , journal =. Stability of entropic optimal transport and

  176. [184]

    On the sample complexity of entropic optimal transport , year =

    Rigollet, Philippe and Stromme, Austin J , journal =. On the sample complexity of entropic optimal transport , year =

  177. [185]

    Limit Theorems for Entropic Optimal Transport Maps and the

    Goldfeld, Ziv and Kato, Kengo and Rioux, Gabriel and Sadhu, Ritwik , journal =. Limit Theorems for Entropic Optimal Transport Maps and the

  178. [186]

    Gradient estimates for the

    Chiarini, Alberto and Conforti, Giovanni and Greco, Giacomo and Tamanini, Luca , journal =. Gradient estimates for the

  179. [187]

    Weak semiconvexity estimates for

    Conforti, Giovanni , journal =. Weak semiconvexity estimates for

  180. [188]

    Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport , year =

    Delalande, Alex , booktitle =. Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport , year =

  181. [189]

    Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem , volume =

    Mena, Gonzalo and Niles-Weed, Jonathan , journal =. Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem , volume =

  182. [190]

    Asymptotics for semidiscrete entropic optimal transport , volume =

    Altschuler, Jason M and Niles-Weed, Jonathan and Stromme, Austin J , journal =. Asymptotics for semidiscrete entropic optimal transport , volume =

  183. [191]

    Log-concave sampling , year =

    Chewi, Sinho , note =. Log-concave sampling , year =

  184. [192]

    Lecture notes on information theory , volume =

    Polyanskiy, Yury and Wu, Yihong , journal =. Lecture notes on information theory , volume =

  185. [193]

    Analysis and geometry of Markov diffusion operators , volume =

    Bakry, Dominique and Gentil, Ivan and Ledoux, Michel and others , publisher =. Analysis and geometry of Markov diffusion operators , volume =

  186. [194]

    Advances in Neural Information Processing Systems , title =

    Janati, Hicham and Muzellec, Boris and Peyr. Advances in Neural Information Processing Systems , title =

  187. [195]

    Estimation of entropy-regularized optimal transport maps between non-compactly supported measures , year =

    Werenski, Matthew and Murphy, James M and Aeron, Shuchin , journal =. Estimation of entropy-regularized optimal transport maps between non-compactly supported measures , year =

  188. [196]

    Boundary regularity of maps with convex potentials , volume =

    Caffarelli, Luis A , journal =. Boundary regularity of maps with convex potentials , volume =

  189. [197]

    Boundary regularity of maps with convex potentials--II , volume =

    Caffarelli, Luis A , journal =. Boundary regularity of maps with convex potentials--II , volume =

  190. [198]

    Interpolating between optimal transport and MMD using

    Feydy, Jean and S. Interpolating between optimal transport and MMD using. The 22nd International Conference on Artificial Intelligence and Statistics , organization =

  191. [199]

    An optimal transport approach for the

    Marino, Simone Di and Gerolin, Augusto , journal =. An optimal transport approach for the

  192. [200]

    Diffusion

    De Bortoli, Valentin and Thornton, James and Heng, Jeremy and Doucet, Arnaud , journal =. Diffusion

  193. [201]

    Meta optimal transport , year =

    Amos, Brandon and Cohen, Samuel and Luise, Giulia and Redko, Ievgen , journal =. Meta optimal transport , year =

  194. [202]

    On amortizing convex conjugates for optimal transport , year =

    Amos, Brandon , journal =. On amortizing convex conjugates for optimal transport , year =

  195. [203]

    Riemannian convex potential maps , year =

    Cohen, Samuel and Amos, Brandon and Lipman, Yaron , booktitle =. Riemannian convex potential maps , year =

  196. [204]

    arXiv preprint arXiv:2209.15621 , title =

    L. arXiv preprint arXiv:2209.15621 , title =

    arXiv

  197. [205]

    Learning single-cell perturbation responses using neural optimal transport , volume =

    Bunne, Charlotte and Stark, Stefan G and Gut, Gabriele and Del Castillo, Jacobo Sarabia and Levesque, Mitch and Lehmann, Kjong-Van and Pelkmans, Lucas and Krause, Andreas and R. Learning single-cell perturbation responses using neural optimal transport , volume =. Nature metho...

  198. [206]

    Semi-Discrete Normalizing Flows through Differentiable Tessellation , year =

    Chen, Ricky TQ and Amos, Brandon and Nickel, Maximilian , journal =. Semi-Discrete Normalizing Flows through Differentiable Tessellation , year =

  199. [207]

    Chin-Wei Huang and Ricky T. Q. Chen and Christos Tsirigotis and Aaron Courville , booktitle =. Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization , url =. 2021 , bdsk-url-1 =

    2021

  200. [208]

    How to train your neural ODE: the world of Jacobian and kinetic regularization , year =

    Finlay, Chris and Jacobsen, J. How to train your neural ODE: the world of Jacobian and kinetic regularization , year =. International Conference on Machine Learning , organization =

  201. [209]

    Ot-flow: Fast and accurate continuous normalizing flows via optimal transport , volume =

    Onken, Derek and Fung, Samy Wu and Li, Xingjian and Ruthotto, Lars , booktitle =. Ot-flow: Fast and accurate continuous normalizing flows via optimal transport , volume =

  202. [210]

    Optimal transport mapping via input convex neural networks , year =

    Makkuva, Ashok and Taghvaei, Amirhossein and Oh, Sewoong and Lee, Jason , booktitle =. Optimal transport mapping via input convex neural networks , year =

  203. [211]

    An Optimal Transport Approach to Causal Inference , year =

    Torous, William and Gunsilius, Florian and Rigollet, Philippe , journal =. An Optimal Transport Approach to Causal Inference , year =

  204. [212]

    Matching for causal effects via multimarginal optimal transport , year =

    Gunsilius, Florian and Xu, Yuliang , journal =. Matching for causal effects via multimarginal optimal transport , year =

  205. [213]

    Supervised Training of Conditional

    Bunne, Charlotte and Krause, Andreas and Cuturi, Marco , journal =. Supervised Training of Conditional

  206. [214]

    Vector quantile regression:

    Carlier, Guillaume and Chernozhukov, Victor and Galichon, Alfred , journal =. Vector quantile regression:

  207. [215]

    Chernozhukov, Victor and Galichon, Alfred and Hallin, Marc and Henry, Marc , journal =. Monge--

  208. [216]

    Optimal transport for diffeomorphic registration , year =

    Feydy, Jean and Charlier, Benjamin and Vialard, Fran. Optimal transport for diffeomorphic registration , year =. International Conference on Medical Image Computing and Computer-Assisted Intervention , organization =

  209. [217]

    Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming , volume =

    Schiebinger, Geoffrey and Shu, Jian and Tabaka, Marcin and Cleary, Brian and Subramanian, Vidya and Solomon, Aryeh and Gould, Joshua and Liu, Siyan and Lin, Stacie and Berube, Peter and others , journal =. Optimal-transport analysis of single-cell gene expression identifies de...

  210. [218]

    An optimal transportation approach for nuclear structure-based pathology , volume =

    Wang, Wei and Ozolek, John A and Slep. An optimal transportation approach for nuclear structure-based pathology , volume =. IEEE transactions on medical imaging , number =

  211. [219]

    Predicting cell lineages using autoencoders and optimal transport , volume =

    Yang, Karren Dai and Damodaran, Karthik and Venkatachalapathy, Saradha and Soylemezoglu, Ali C and Shivashankar, GV and Uhler, Caroline , journal =. Predicting cell lineages using autoencoders and optimal transport , volume =

  212. [220]

    Unsupervised Integration of Single-Cell Multi-omics Datasets with Disproportionate Cell-Type Representation , year =

    Demet. Unsupervised Integration of Single-Cell Multi-omics Datasets with Disproportionate Cell-Type Representation , year =. International Conference on Research in Computational Molecular Biology , organization =

  213. [221]

    NovoSpaRc: flexible spatial reconstruction of single-cell gene expression with optimal transport , volume =

    Moriel, Noa and Senel, Enes and Friedman, Nir and Rajewsky, Nikolaus and Karaiskos, Nikos and Nitzan, Mor , journal =. NovoSpaRc: flexible spatial reconstruction of single-cell gene expression with optimal transport , volume =

  214. [222]

    Ffjord: Free-form continuous dynamics for scalable reversible generative models , year =

    Grathwohl, Will and Chen, Ricky TQ and Bettencourt, Jesse and Sutskever, Ilya and Duvenaud, David , journal =. Ffjord: Free-form continuous dynamics for scalable reversible generative models , year =

  215. [223]

    Improving

    Tim Salimans and Han Zhang and Alec Radford and Dimitris Metaxas , booktitle =. Improving

  216. [224]

    Proceedings of the 34th International Conference on Machine Learning , pages =

    Martin Arjovsky and Soumith Chintala and L. Proceedings of the 34th International Conference on Machine Learning , pages =

  217. [225]

    Entropic metric alignment for correspondence problems , volume =

    Justin Solomon and Gabriel Peyr. Entropic metric alignment for correspondence problems , volume =. 2016 , bdsk-url-1 =

    2016

  218. [226]

    Simulation-free

    Tong, Alexander and Malkin, Nikolay and Fatras, Kilian and Atanackovic, Lazar and Zhang, Yanlei and Huguet, Guillaume and Wolf, Guy and Bengio, Yoshua , journal=. Simulation-free

  219. [227]

    Convolutional

    Solomon, Justin and De Goes, Fernando and Peyr. Convolutional. ACM Transactions on Graphics (TOG) , number =

  220. [228]

    Weak convergence and empirical processes with applications to statistics , year =

    Vaart, Aad W and Wellner, Jon A , booktitle =. Weak convergence and empirical processes with applications to statistics , year =

  221. [229]

    High-dimensional probability: An introduction with applications in data science , volume =

    Vershynin, Roman , publisher =. High-dimensional probability: An introduction with applications in data science , volume =

  222. [230]

    Asymptotic analysis of the exponential penalty trajectory in linear programming , volume =

    Cominetti, Roberto and Mart. Asymptotic analysis of the exponential penalty trajectory in linear programming , volume =. Mathematical Programming , number =

  223. [231]

    arXiv preprint arXiv:2202.10434 , title =

    Hundrieser, Shayan and Staudt, Thomas and Munk, Axel , date-modified =. arXiv preprint arXiv:2202.10434 , title =

    arXiv

  224. [232]

    The union of manifolds hypothesis and its implications for deep generative modelling , year =

    Brown, Bradley CA and Caterini, Anthony L and Ross, Brendan Leigh and Cresswell, Jesse C and Loaiza-Ganem, Gabriel , journal =. The union of manifolds hypothesis and its implications for deep generative modelling , year =

  225. [233]

    Testing the manifold hypothesis , volume =

    Fefferman, Charles and Mitter, Sanjoy and Narayanan, Hariharan , journal =. Testing the manifold hypothesis , volume =

  226. [234]

    Non-asymptotic convergence bounds for

    M\'. Non-asymptotic convergence bounds for. Advances in Neural Information Processing Systems , editor =

  227. [235]

    Ricky T. Q. Chen and Brandon Amos and Maximilian Nickel , booktitle =. Semi-Discrete Normalizing Flows through Differentiable Tessellation , year =

  228. [236]

    Foundations of quantization for probability distributions , year =

    Graf, Siegfried and Luschgy, Harald , publisher =. Foundations of quantization for probability distributions , year =

  229. [237]

    High-dimensional statistics: A non-asymptotic viewpoint , volume =

    Wainwright, Martin J , publisher =. High-dimensional statistics: A non-asymptotic viewpoint , volume =

  230. [238]

    and Zemel, Yoav , booktitle =

    Panaretos, Victor M. and Zemel, Yoav , booktitle =. The Wasserstein Space , year =

  231. [239]

    Gradient flows in metric spaces and in the space of probability measures , year =

    Ambrosio, Luigi and Gigli, Nicola and Savar\'. Gradient flows in metric spaces and in the space of probability measures , year =

  232. [240]

    Localization schemes: a framework for proving mixing bounds for

    Chen, Yuansi and Eldan, Ronen , booktitle =. Localization schemes: a framework for proving mixing bounds for

  233. [241]

    An entropy approach to the time reversal of diffusion processes , volume =

    F\". An entropy approach to the time reversal of diffusion processes , volume =. Stochastic differential systems (

  234. [242]

    2024 , howpublished =

    2024

  235. [243]

    , title =

    Chen, S. , title =. 2017 , howpublished =

    2017

  236. [244]

    Moon, K. R. and van Dijk, D. and Wang, Z. and Gigante, S. and Burkhardt, D. B. and Chen, W. S. and Yim, K. and Elzen, A. v. d. and Hirn, M. J. and Coifman, R. R. and Ivanova, N. B. and Wolf, G. and Krishnaswamy, S. , title =. Nature Biotechnology , volume =. 2019 , doi =

    2019

  237. [245]

    and Luecken, M

    Burkhardt, D. and Luecken, M. and Benz, A. and Holderrieth, P. and Bloom, J. and Lance, C. and Chow, A. and Holbrook, R. , title =. 2022 , howpublished =

    2022

  238. [246]

    Proceedings of the 43rd International Conference on Machine Learning , year =

    Kansal, Raghav and Crair, David and Nguyen, Nghia and Pope, Scott and Parry, Bradley , title =. Proceedings of the 43rd International Conference on Machine Learning , year =. 2606.05327 , archivePrefix =

    arXiv

  239. [247]

    and Huang, J

    Tong, A. and Huang, J. and Wolf, G. and van Dijk, D. and Krishnaswamy, S. , title =. Proceedings of the 37th International Conference on Machine Learning , volume =. 2020 , url =

    2020

  240. [248]

    and Potaptchik, P

    Kapusniak, K. and Potaptchik, P. and Reu, T. and Zhang, L. and Tong, A. and Bronstein, M. M. and Bose, J. and Giovanni, F. D. , title =. The Thirty-eighth Annual Conference on Neural Information Processing Systems , year =

  241. [249]

    and Jiang, Y

    Wang, D. and Jiang, Y. and Zhang, Z. and Gu, X. and Zhou, P. and Sun, J. , title =. The Thirty-ninth Annual Conference on Neural Information Processing Systems , year =

  242. [250]

    and Brekelmans, R

    Neklyudov, K. and Brekelmans, R. and Tong, A. and Atanackovic, L. and Liu, Q. and Makhzani, A. , title =. Proceedings of the 41st International Conference on Machine Learning , editor =. 2024 , url =

    2024

  243. [251]

    and Ba, Jimmy , title =

    Kingma, Diederik P. and Ba, Jimmy , title =. 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings , editor =. 2015 , url =

    2015

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