Pith. sign in

REVIEW 3 major objections 5 minor 71 references

Joint Flow Matching makes a single reversible flow both a generator and a classifier, with a provable consistency relation between the two conditionals.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-07-31 23:27 UTC pith:Z4VPQXSI

load-bearing objection Neat idea with a sound consistency theorem, but the experiments violate the theorem's key assumption and the empirical comparison is too thin to carry the claims. the 3 major comments →

arxiv 2607.23946 v1 pith:Z4VPQXSI submitted 2026-07-27 cs.LG

Joint Flow Matching for Generator-Consistent Classification

Hayden McAlister , Lech Szymanski This is my paper
classification cs.LG
keywords joint flow matchingcontinuous normalising flowsconditional generationclassificationgenerative-discriminative consistencyconfidence calibrationmodel interpretabilityflow matching
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Joint Flow Matching (JFM) trains a continuous normalising flow over paired variables, such as images and labels, by assigning them opposite temporal roles: image noise flows to real images while real labels flow to label noise. As a result, integrating the same flow forward generates images from labels, and integrating backward classifies images. The paper proves that both directions sample the two conditionals of a single induced joint distribution, yielding the exact consistency identity pJFM(x|y)p_data(y) = pJFM(y|x)p_data(x). This gives a single model whose generative and discriminative behaviours cannot disagree, without a separate classifier or approximate inference. On MNIST and CIFAR-10, the authors report competitive accuracy with naturally calibrated confidence, and they use the consistency to interpret which image features drive class decisions.

Core claim

The central claim is that placing image and label variables at opposite temporal endpoints turns one continuous normalising flow into both a generator and a classifier. With endpoint distributions p0(x,y)=p_noise(x)p_data(y) and p1(x,y)=p_data(x)p_noise(y), the flow implicitly defines a joint distribution pJFM as the pair of the forward-flow image output and the label input. Because the flow is reversible, integrating forward from a label samples pJFM(x|y), and integrating backward from an image samples pJFM(y|x), with the consistency identity pJFM(x|y)p_data(y)=pJFM(y|x)p_data(x) holding exactly. This is internal consistency: pJFM is the coupling induced by the trained flow, not necessarily

What carries the argument

The load-bearing object is the map Psi(x0,y0) = (pi_x(Phi_1(x0,y0)), y0), which pairs the image at the end of the forward flow with the label at its start, and its pushforward pJFM = Psi_* p0. This map isolates the learned coupling between image and label in one joint distribution; the consistency relation then follows from Bayes' theorem applied to that joint. The construction works because one variable travels noise-to-data while the other travels data-to-noise across the same time interval, so a single ODE provides both conditional directions.

Load-bearing premise

The load-bearing premise is that each label slice acts like a one-to-one smooth map — no two different noise inputs with the same label land on the same image — combined with treating one-hot labels as continuous variables; if either fails, the joint density and the consistency identity are not well-defined.

What would settle it

On a trained JFM model, reverse-flow a fixed set of images with many label-noise samples to estimate pJFM(y|x), then forward-flow many noise samples from those labels to estimate pJFM(x|y), and check whether pJFM(x|y)p_data(y) equals pJFM(y|x)p_data(x) within Monte Carlo error; a systematic mismatch would falsify the consistency claim. Separately, look for two distinct noise seeds with the same label that flow to nearly identical images — frequent collisions would violate the slice-diffeomorphism assumption.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A single trained JFM model performs class-conditional generation and classification without a separate classifier or approximate inference, with a guaranteed consistency between the two.
  • The consistency relation holds for any velocity model satisfying the endpoint conditions, so trajectory straightening or optimal-transport couplings can be added without breaking the guarantee.
  • Reverse flow recovers a class-independent noise vector from an image; re-flowing that noise with a different label swaps class while preserving context, yielding counterfactual visualisations from the same model.
  • Confidence scores are naturally calibrated without post-hoc calibration in the reported experiments: ECE 0.003 on MNIST and 0.057 on CIFAR-10.
  • The induced joint pJFM gives a model-internal view of what a classifier relies on: grouping generated images by reverse-flow confidence reveals features that drive class decisions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This consistency suggests a benchmark for post-hoc explainability: a saliency method should agree with the features that actually change when JFM re-flows an image's recovered noise under a different label.
  • Because pJFM is model-internal, 'consistent' means internally coupled, not externally correct; this distinction, noted in the paper, is easy to miss and should be highlighted in any application.
  • Extending JFM to continuous Y for regression or structured outputs is natural; the paper leaves that reverse conditional uncharacterised, so the first check would be whether Eq. 7 holds empirically for continuous targets.
  • The slice-diffeomorphism assumption can be tested directly by searching for collisions in forward integration from different noise seeds with the same label; non-negligible collisions would break the density derivation.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper introduces Joint Flow Matching (JFM), a continuous normalising flow framework for paired variables (X,Y). The key design is to assign the data distribution of X and the noise distribution of Y at t=0, and the noise distribution of X and the data distribution of Y at t=1. The paper defines an induced joint distribution pJFM over (x1,y0) and claims that forward integration (generation) and backward integration (classification) through the same flow yield the conditionals pJFM(x1|y0) and pJFM(y0|x1), giving a provable consistency between generation and classification (Eq. 7). The authors prove this under a slice-diffeomorphism assumption and validate on a spiral toy problem, MNIST, and CIFAR-10, reporting competitive accuracy and low expected calibration error.

Significance. The idea of exploiting opposite endpoint roles to obtain bidirectional consistency from a single flow is elegant and, to my knowledge, novel. The core change-of-variables derivation for the continuous case is sound, and the paper correctly identifies that the consistency relation is internal to the model rather than a statement about matching the true data distribution. The empirical results show the framework can be trained on standard image benchmarks and that calibration emerges without post-hoc processing; the interpretability applications (Figures 3 and 4) are suggestive. However, the central guarantee is formulated for continuous densities, while the main classification experiments use discrete one-hot labels, so the provable consistency claim does not apply to the paper's primary setting. This gap is not merely cosmetic and must be addressed before the claims can be accepted.

major comments (3)
  1. [§2.2, Eq. (6)-(7); §4.2] The theory assumes p0 and p1 have densities w.r.t. Lebesgue measure. In the classification experiments, pdata(Y) is discrete on one-hot vectors, so p0 is supported on a finite union of D-dimensional affine subspaces of R^{D+K}. Since Φ1 is a diffeomorphism, (Φ1)_*p0 is also singular, and cannot equal p1 = pdata(X)N(0, σ_yI), which is absolutely continuous. Thus the endpoint condition cannot be exactly satisfied, Eq. (6) is not valid, and Eq. (7) is not defined. The manuscript acknowledges the discreteness in §4.2 but does not reconcile it with the theory; the statement that the formulation was 'sufficient' does not rescue the provable-consistency claim for MNIST/CIFAR-10. Please provide a rigorous treatment (e.g., formalize the model with label noise/smoothing so Y has a density) or restrict the theorem to continuous Y and reframe the experimental claims as an approximation.
  2. [§2.3] The proof of the backward direction is only a sketch. The sentence 'by bijectivity of Φ1' is not enough to show that sampling y1~pnoise(Y) and inverting the flow yields pJFM(y0|x1). Please write out the full argument: since (x1,y1) ~ p1 implies (x0,y0)=Φ^{-1}(x1,y1) ~ p0, and pJFM = Ψ_*p0 with Ψ(x0,y0)=(πxΦ1(x0,y0),y0), the induced distribution of (x1,y0) under this sampling scheme is exactly pJFM; the conditional then follows. This derivation also clarifies where the slice-diffeomorphism assumption is used.
  3. [§2.2] The slice-diffeomorphism assumption, that πx∘Φ1(·,y0) is a diffeomorphism for almost every y0, is essential for Eq. (6) yet is stated to be not derivable from ODE regularity. Since the paper's central formal object pJFM is defined through this map, the assumption should be either proved under suitable conditions or empirically verified (e.g., by checking invertibility of the slice Jacobian on test labels). As written, the abstract's unconditional 'We prove' overstates the result.
minor comments (5)
  1. [§4.2] The sentence 'We trained U-Net to model the objective described in Equation 7 using the loss defined in Equation 8' is confusing; the objective is defined in Equation 1 or 8, not 7.
  2. [Related Work] Typo: 'mutliple' should be 'multiple'; 'form a set' should be 'from a set'. Also, the citation 'CycleGAN Zhao et al. [2020]' appears to mis-attribute the CycleGAN method; the cited paper is not the original CycleGAN paper (Zhu et al., 2017).
  3. [§2.2] The phrase 'or equivalently the Y-output of the reverse flow paired with the Y-input' should read 'paired with the X-input'.
  4. [Conclusion] Typo: 'JMF' should be 'JFM'.
  5. [Eq. (7)] Clarify that the equality holds exactly only under the ideal endpoint condition (Φ1)_*p0 = p1; in practice it is an approximate identity, since pJFM's x1-marginal may differ from pdata(x1) under approximate training.

Circularity Check

0 steps flagged

No significant circularity: JFM's consistency guarantee is a formal theorem from the definition of pJFM and flow bijectivity, not a fitted prediction or self-citation chain.

full rationale

The central consistency claim (Eq. 7) is derived, not fitted. pJFM is explicitly defined as Ψ_*p0 (Eqs. 5-6), so forward sampling x1|y0 is pJFM(x1|y0) by definition; the paper states this directly ('Both claims follow directly from the definition of pJFM as Ψ∗p0'). The backward direction is the substantive step: it uses bijectivity of Φ1 and the endpoint condition (Φ1)_*p0 = p1 to recover the same conditional pJFM(y0|x1) and to identify the marginals with pdata, yielding Bayes' identity. No trainable parameters are fit to enforce consistency; the result holds for any diffeomorphic flow satisfying the endpoint conditions. There are no load-bearing self-citations (the paper has no self-citations), no imported uniqueness theorem, and no ansatz smuggled in via citation. The acknowledged limitations—the slice-diffeomorphism assumption (§2.2) and the use of discrete one-hot labels (§4.2, §5.2)—are correctness/assumption gaps that can invalidate the density derivation in practice, but they are not circular: they do not make Eq. 7 an input to itself. Hence score 0.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 1 invented entities

The central theorem depends on standard flow-matching equivalence, ODE regularity, and the explicitly stated slice-diffeomorphism assumption. The discrete-label approximation is another domain-level premise. No fitted constants are used to derive the consistency property; σy and the MC sample count are hyperparameters affecting the empirical calibration claims.

free parameters (3)
  • label noise scale σy = 0.1
    Hand-chosen; controls the reverse-flow label noise distribution and therefore the stochastic classifier's confidence scores and ECE calibration (§4.2).
  • image noise scale σx = 1.0
    Hand-chosen; standard for flow matching; not central to the consistency claim.
  • number of Monte Carlo samples for confidence = 10
    Confidence is the empirical frequency of the modal prediction over 10 samples of y1; this coarse resolution affects the ECE estimate (§5.2).
axioms (4)
  • standard math Standard flow matching theory: minimizing the conditional flow matching loss (Eq. 8) is equivalent to learning the marginal vector field that pushes p0 to p1.
    Invoked in §2.4 following Lipman et al. [2023]; not re-derived.
  • standard math Regularity conditions on v ensure Φt is a diffeomorphism for each t.
    Used in §2.2 for the change-of-variables formula; standard ODE result not proven.
  • domain assumption Slice-diffeomorphism: for almost every y0, πx∘Φ1(·,y0) is a diffeomorphism.
    Assumed in §2.2 to justify Eq. 6; the paper admits it is not derivable from ODE regularity conditions; load-bearing for the pJFM density and the consistency proof.
  • domain assumption One-hot label vectors with Gaussian noise approximate a continuous endpoint distribution.
    Used in §4.2; p_data(Y) is discrete but treated as continuous via one-hot encoding; flow matching on delta measures is not well-defined, so this is an approximation.
invented entities (1)
  • pJFM(X,Y) joint distribution independent evidence
    purpose: Defines the coupling between generated images x1 and label scores y0 induced by the flow; the key object in the consistency guarantee.
    It has falsifiable consequences: forward and reverse conditionals of a trained model should match, which the spiral experiment tests. Not a physical entity but a new mathematical construct.

pith-pipeline@v1.3.0-alltime-deepseek · 11750 in / 23983 out tokens · 194590 ms · 2026-07-31T23:27:15.072358+00:00 · methodology

0 comments
read the original abstract

We introduce Joint Flow Matching (JFM), a training framework for continuous normalising flows over multiple variables. Standard flow matching transports variables from noise to data simultaneously, offering no natural mechanism for forward and reverse conditional inference from a shared joint model. JFM resolves this by assigning opposite roles to each variable at the temporal endpoints. We prove that JFM produces a consistent joint distribution where that forward or reverse integration are conditionals of the same joint. We explore this consistency in the context of joint classification and generation as the basis for interpretability in discriminative-generative models. We validate JFM on conditional datasets producing competitive accuracy with inherently well-calibrated confidence scores without post-hoc calibration, and classifier-consistent image generation.

Figures

Figures reproduced from arXiv: 2607.23946 by Hayden McAlister, Lech Szymanski.

Figure 1
Figure 1. Figure 1: Forward flow in FM and JFM trained to model [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the consistency of JFM. A flow is trained on the marginal distributions along [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: CIFAR-10 images JFM-generated from the noise [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Generated examples for select CIFAR10 classes grouped by confidence of the reverse-flow [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Reverse flow in FM and JFM trained to model [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Classification decisions and confidence of the JFM trained on MNIST data evaluated on [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Classification decisions and confidence of the JFM trained on CIFAR10 data evaluated on [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Generated examples for remaining CIFAR10 classes (continued from Figure 4) grouped by [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

71 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    Albergo, Michael S. and. Building. doi:10.48550/arXiv.2209.15571 , archiveprefix =. 2209.15571 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.2209.15571

  2. [2]

    and Welling, Max , year = 2019, number =

    van den Berg, Rianne and Hasenclever, Leonard and Tomczak, Jakub M. and Welling, Max , year = 2019, number =. Sylvester. doi:10.48550/arXiv.1803.05649 , archiveprefix =. 1803.05649 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.1803.05649 2019

  3. [3]

    Bertrand, Quentin and Gagneux, Anne and Massias, Mathurin and Emonet, R. On the

  4. [4]

    Chen, Ricky T. Q. and Rubanova, Yulia and Bettencourt, Jesse and Duvenaud, David K , year = 2018, volume =. Neural. Advances in

    2018

  5. [5]

    Chen, Ricky T. Q. and Lipman, Yaron , year = 2024, booktitle =. Flow

    2024

  6. [6]

    doi:10.48550/arXiv.1410.8516 , archiveprefix =

    Dinh, Laurent and Krueger, David and Bengio, Yoshua , year = 2015, number =. doi:10.48550/arXiv.1410.8516 , archiveprefix =. 1410.8516 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.1410.8516 2015

  7. [7]

    Density Estimation Using

    Dinh, Laurent and. Density Estimation Using

  8. [8]

    TO-FLOW: Efficient Continuous Normalizing Flows with Temporal Optimization adjoint with Moving Speed

    Du, Shian and Luo, Yihong and Chen, Wei and Xu, Jian and Zeng, Delu , year = 2022, number =. doi:10.48550/arXiv.2203.10335 , archiveprefix =. 2203.10335 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2203.10335 2022

  9. [9]

    Gagneux, Anne and Martin, S. The. arXiv preprint arXiv:s2510.24830 , eprint =

    arXiv

  10. [10]

    Grathwohl, Will and Chen, Ricky T. Q. and Bettencourt, Jesse and Sutskever, Ilya and Duvenaud, David , year = 2019, booktitle=

    2019

  11. [11]

    2511.20462 , primaryclass =

    Gu, Jiatao and Shen, Ying and Chen, Tianrong and Dinh, Laurent and Wang, Yuyang and Bautista, Miguel Angel and Berthelot, David and Susskind, Josh and Zhai, Shuangfei , year = 2025, journal =. 2511.20462 , primaryclass =

    arXiv 2025

  12. [12]

    Gu, Jiatao and Chen, Tianrong and Berthelot, David and Zheng, Huangjie and Wang, Yuyang and Zhang, Ruixiang and Dinh, Laurent and Bautista, Miguel Angel and Susskind, Josh and Zhai, Shuangfei , year =

  13. [13]

    Generalization in Diffusion Models Arises from Geometry-Adaptive Harmonic Representations , author =

  14. [14]

    and Dhariwal, Prafulla , year = 2018, number =

    Kingma, Diederik P. and Dhariwal, Prafulla , year = 2018, number =. Glow:. doi:10.48550/arXiv.1807.03039 , archiveprefix =. 1807.03039 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.1807.03039 2018

  15. [15]

    and Salimans, Tim and Jozefowicz, Rafal and Chen, Xi and Sutskever, Ilya and Welling, Max , year = 2016, booktitle =

    Kingma, Diederik P. and Salimans, Tim and Jozefowicz, Rafal and Chen, Xi and Sutskever, Ilya and Welling, Max , year = 2016, booktitle =. Improving

    2016

  16. [16]

    Neural Information Processing Systems , author =

    Optimal. Neural Information Processing Systems , author =

  17. [17]

    Kumar, Manoj and Babaeizadeh, Mohammad and Erhan, Dumitru and Finn, Chelsea and Levine, Sergey and Dinh, Laurent and Kingma, Durk , year = 2020, booktitle=

    2020

  18. [18]

    A Survey of the

    L. A Survey of the. doi:10.48550/arXiv.1308.0215 , archiveprefix =. 1308.0215 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.1308.0215

  19. [19]

    International Conference on Learning Representations , year=

    Flow Matching for Generative Modeling , author=. International Conference on Learning Representations , year=

  20. [20]

    Lipman, Yaron and Chen, Ricky T. Q. and. Flow

  21. [21]

    International Conferenceon Learning Representations , author =

    Flow. International Conferenceon Learning Representations , author =

  22. [22]

    Towards a

    Niedoba, Matthew and Zwartsenberg, Berend and Murphy, Kevin and Wood, Frank , year = 2025, booktitle=. Towards a

    2025

  23. [23]

    and Chen, Ricky T

    Pokle, Ashwini and Muckley, Matthew J. and Chen, Ricky T. Q. and Karrer, Brian , year = 2024, number =. Training-Free. doi:10.48550/arXiv.2310.04432 , archiveprefix =. 2310.04432 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.2310.04432 2024

  24. [24]

    International Conference on Machine Learning , author =

    Multisample. International Conference on Machine Learning , author =

  25. [25]

    Variational

    Rezende, Danilo Jimenez and Mohamed, Shakir , year = 2015, booktitle =. Variational

    2015

  26. [26]

    Tabak, E. G. and Turner, Cristina V. , year = 2013, journal =. A

    2013

  27. [27]

    and Welling, Max , year = 2017, number =

    Tomczak, Jakub M. and Welling, Max , year = 2017, number =. Improving. doi:10.48550/arXiv.1611.09630 , archiveprefix =. 1611.09630 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.1611.09630 2017

  28. [28]

    Improving and Generalizing Flow-Based Generative Models with Minibatch Optimal Transport , author =

  29. [29]

    Generalization through Variance: How Noise Shapes Inductive Biases in Diffusion Models , author =

  30. [30]

    Zhang, Yasi and Yu, Peiyu and Zhu, Yaxuan and Chang, Yingshan and Gao, Feng and Wu, Ying Nian and Leong, Oscar , booktitle =. Flow

  31. [31]

    Goodfellow, Ian J. and. Generative. Advances in

  32. [32]

    and Sutton, Charles , year = 2017, volume =

    Srivastava, Akash and Valkov, Lazar and Russell, Chris and Gutmann, Michael U. and Sutton, Charles , year = 2017, volume =. Advances in

    2017

  33. [33]

    Catastrophic Forgetting and Mode Collapse in

  34. [34]

    and Rezende, Danilo J

    Kingma, Diederik P. and Rezende, Danilo J. and Mohamed, Shakir and Welling, Max , year = 2014, volume =. Semi-Supervised. Advances in

    2014

  35. [35]

    Denoising

    Ho, Jonathan and Jain, Ajay and Abbeel, Pieter , year = 2020, volume =. Denoising. Advances in

    2020

  36. [36]

    International Conference on Machine Learning , author =

    Deep. International Conference on Machine Learning , author =

  37. [37]

    Generative

    Song, Yang and Ermon, Stefano , year = 2019, journal =. Generative

    2019

  38. [38]

    Song, Yang and. Score-

  39. [39]

    Diffusion

    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 , year = 2023, journal =. Diffusion

    2023

  40. [40]

    Implicit

    Du, Yilun and Mordatch, Igor , year = 2019, volume =. Implicit. Advances in

    2019

  41. [41]

    , year = 2021, journal =

    Song, Yang and Kingma, Diederik P. , year = 2021, journal =. How to. 2101.03288 , primaryclass =

    Pith/arXiv arXiv 2021

  42. [42]

    International Conference Machine Learning , author =

    Learning the. International Conference Machine Learning , author =

  43. [43]

    Grathwohl, Will and Kelly, Jacob and Hashemi, Milad and Norouzi, Mohammad and Swersky, Kevin and Duvenaud, David , year = 2021, booktitle=. No

    2021

  44. [44]

    Structured

    Lu, You and Huang, Bert , year = 2020, journal =. Structured. doi:10.1609/aaai.v34i04.5940 , copyright =

    work page doi:10.1609/aaai.v34i04.5940 2020

  45. [45]

    Sorkhei, Moein and Henter, Gustav Eje and Kjellstr. Full-. Pattern. doi:10.1007/978-3-030-92659-5_45 , isbn =

    work page doi:10.1007/978-3-030-92659-5_45

  46. [46]

    Classifier-

    Ho, Jonathan and Salimans, Tim , booktitle=. Classifier-

  47. [47]

    Li, Xiao-Hui and Shi, Yuhan and Li, Haoyang and Bai, Wei and Cao, Caleb Chen and Chen, Lei , year = 2021, pages =. An. Proceedings of the

    2021

  48. [48]

    Simonyan, Karen and Vedaldi, Andrea and Zisserman, Andrew , year = 2014, journal =. Deep. 1312.6034 , primaryclass =

    Pith/arXiv arXiv 2014

  49. [49]

    and Fergus, Rob , editor =

    Zeiler, Matthew D. and Fergus, Rob , editor =. Visualizing and. Computer

  50. [50]

    Proceedings of the

    Goetschalckx, Lore and Andonian, Alex and Oliva, Aude and Isola, Phillip , year = 2019, pages =. Proceedings of the

    2019

  51. [51]

    Lundberg, Scott M and Lee, Su-In , year = 2017, volume =. A. Advances in

    2017

  52. [52]

    Axiomatic

    Sundararajan, Mukund and Taly, Ankur and Yan, Qiqi , year = 2017, pages =. Axiomatic. Proceedings of the

    2017

  53. [53]

    Ronneberger, Olaf and Fischer, Philipp and Brox, Thomas , year = 2015, number =. U-. doi:10.48550/arXiv.1505.04597 , archiveprefix =. 1505.04597 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.1505.04597 2015

  54. [54]

    Attention Is

    Vaswani, Ashish and Shazeer, Noam and Parmar, Niki and Uszkoreit, Jakob and Jones, Llion and Gomez, Aidan N and Kaiser,. Attention Is. Advances in

  55. [55]

    Ioffe, Sergey and Szegedy, Christian , year = 2015, booktitle =. Batch

    2015

  56. [56]

    He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian , booktitle =. Deep

  57. [57]

    Dropout as a

    Gal, Yarin and Ghahramani, Zoubin , year = 2015, number =. Dropout as a. doi:10.48550/arXiv.1506.02142 , archiveprefix =. 1506.02142 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.1506.02142 2015

  58. [58]

    Scalable

    Peebles, William and Xie, Saining , year = 2023, number =. Scalable. doi:10.48550/arXiv.2212.09748 , archiveprefix =. 2212.09748 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.2212.09748 2023

  59. [59]

    Learning

    Krizhevsky, Alex and Hinton, Geoffrey , year = 2009, journal =. Learning

    2009

  60. [60]

    LeCun, Yann and Cortes, Corrina and Burges, Christopher , year = 1998, keywords =

    1998

  61. [61]

    and Ba, Jimmy , year = 2017, number =

    Kingma, Diederik P. and Ba, Jimmy , year = 2017, number =. Adam:. doi:10.48550/arXiv.1412.6980 , archiveprefix =. 1412.6980 , publisher =

    Pith/arXiv arXiv doi:10.48550/arxiv.1412.6980 2017

  62. [62]

    , year = 2016, volume =

    Krotov, Dmitry and Hopfield, John J. , year = 2016, volume =. Dense. Advances in

    2016

  63. [63]

    Krotov, Dmitry and Hopfield, John , year = 2018, journal =. Dense. doi:10.1162/neco_a_01143 , keywords =

    work page doi:10.1162/neco_a_01143 2018

  64. [64]

    Learning with

    Seeger, Matthias , year = 2000, langid =. Learning with

    2000

  65. [65]

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

    One Transformer Fits All Distributions in Multi-Modal Diffusion at Scale , author =. Proceedings of the 40th International Conference on Machine Learning , pages =. 2023 , editor =

    2023

  66. [66]

    Text-to-Image Diffusion Models are Zero Shot Classifiers , volume =

    Clark, Kevin and Jaini, Priyank , booktitle =. Text-to-Image Diffusion Models are Zero Shot Classifiers , volume =

  67. [67]

    and Prabhudesai, Mihir and Duggal, Shivam and Brown, Ellis and Pathak, Deepak , title =

    Li, Alexander C. and Prabhudesai, Mihir and Duggal, Shivam and Brown, Ellis and Pathak, Deepak , title =. Proceedings of the IEEE/CVF International Conference on Computer Vision , year =

  68. [68]

    Arnold and S

    Barry C. Arnold and S. James Press , title =. Journal of the American Statistical Association , volume =. 1989 , publisher =

    1989

  69. [69]

    Proceedings of the European Conference on Computer Vision , pages =

    Zhao, Yihao and Wu, Ruihai and Dong, Hao , title =. Proceedings of the European Conference on Computer Vision , pages =. 2020 , publisher =

    2020

  70. [70]

    Diffusion Models Beat GANs on Image Synthesis , volume =

    Dhariwal, Prafulla and Nichol, Alexander , booktitle =. Diffusion Models Beat GANs on Image Synthesis , volume =

  71. [71]

    and van der Sommen, Fons , title =

    Caetano, Francisco and Viviers, Christiaan and De With, Peter H.N. and van der Sommen, Fons , title =. Proceedings of the AAAI Conference on Artificial Intelligence , articleno =. 2026 , publisher =

    2026