Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Distributional Diffusion Models with Scoring Rules

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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

Pith's one-line read This paper proposes to accelerate diffusion sampling by training the denoiser to generate from the full posterior of clean data given noisy data, via a generalized energy score, instead of predicting only the conditional mean.

desk verdict A clean, useful diffusion training loss that learns the full posterior and helps at few steps, with an overclaimed abstract and a core mechanism only directly validated in 2D. read the letter →

arxiv 2502.02483 v3 pith:KT6DH7YV submitted 2025-02-04 cs.LG stat.ML

Valentin De Bortoli , Alexandre Galashov , J. Swaroop Guntupalli , Guangyao Zhou , Kevin Murphy , Arthur Gretton , Arnaud Doucet This is my paper · ORCID
classification cs.LGstat.ML
keywords distributionaldiffusionmodelsscoringrulesgeneralizedenergyscorefew-stepsamplingconditionalposteriorlearningkernelscoresaccelerationgenerativemodeling
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

Diffusion models generate data by reversing a noise-corruption process, but each reverse step only predicts the mean of the clean data consistent with the noisy input, and that mean is a poor stand-in when few steps are taken. This paper proposes to train the denoiser to output samples from the whole conditional distribution of clean data given noisy data, using a generalized energy score as the training loss. The central claim is that this distributional training allows the reverse process to be run on a coarse time scale: with few denoising steps, models trained with λ=1 and β<2 outperform classical diffusion models on images and robot trajectory tasks, while with many steps the classical regression loss remains best and the hyperparameter λ interpolates between the two regimes. The practical change is nearly drop-in: the network simply receives an extra noise input, concatenated along the channel dimension, and the same DDIM-style sampler is reused.

What carries the argument

The load-bearing object is the conditional generalized energy score, S_{λ,β}(p, y) = (λ/2)E_{p⊗p}[||X−X'||^β] − E_p[||X−y||^β], a proper scoring rule that scores a predicted distribution p against an observed y and is strictly proper for λ=1 and β∈(0,2), meaning the true posterior uniquely maximizes it. The training loss integrates this score over noise levels and samples, and the two hyperparameters have concrete roles: β sets the distance metric — with β→2 the score degenerates to the squared-error regression loss and with small β it behaves like a heavy-tailed energy distance — while λ trades off the score's two terms, with λ=1 enforcing full posterior fidelity and λ<1 deliberately underestimating the posterior variance by the factor f(λ,β) = ($2λ^{{−2/(2−β)}}$ − 1)^{−1} (Proposition 4.1). At inference, the intractable reverse transition p(x_s|x_t) = ∫ p(x_s|x_0,x_t) p(x_0|x_t) dx_0 is approximated by a single Monte Carlo draw: sample x̂_0 = x̂θ(t, x_t, ξ) and plug it into the closed-form Gaussian conditional p(x_s|x̂_0, x_t) of Eq. (4), which is the only change to the standard DDIM sampler.

What would settle it

On a target whose reverse posterior is genuinely multimodal at an intermediate noise level — for example a two-Gaussian mixture in 10 dimensions whose modes are separated by many times σ at t=0.5 — sample x̂_0 = x̂θ(t, x_t, ξ) for a fixed x_t and many ξ, and compare the empirical distribution of the draws with the exact p(x_0|x_t): if the draws systematically miss a mode that carries substantial posterior mass, the single-sample plug-in provably loses probability mass, and the few-step gains would not survive on such targets.

Watch

Extended reading notes

Core claim

The paper's central claim is that the failure of diffusion models at few sampling steps is caused by the Dirac approximation of the posterior p_{0|t}(x_0|x_t): replacing the full posterior by a point mass at the conditional mean E[X_0|X_t=x_t] is only justified in the infinite-step limit. To remove that approximation, the paper replaces the regression loss with a conditional generalized energy score S_{λ,β}(p^θ_{0|t}(·|x_t), x_0) = (λ/2) E_{p^θ⊗p^θ}[||X−X'||^β] − E_{p^θ}[||X−x_0||^β], which is strictly proper for λ=1 and β∈(0,2) and which reduces to the classical regression loss as β→2, λ→0. The trained generator x̂θ(t, x_t, ξ) then supplies samples from the learned posterior, and Algorithm 2 uses one such sample in the Gaussian conditional p(x_s|x̂_0, x_t) to step the reverse process on a coarse grid. Empirically, the paper finds that distributional models with λ=1, β<2 achieve the best FID and robot success rates when the number of denoising steps is low, that λ<1 increasingly wins as the step count grows, and that even λ=0 with β<2 matches or slightly beats the classical squared-error loss.

Load-bearing premise

Everything hinges on Algorithm 2's single-sample plug-in: the intractable reverse transition is replaced by one random draw from the learned posterior x̂θ(t, x_t, ξ), and the paper provides no error bound for this replacement when the true posterior is not Gaussian, so the method's correctness depends on the learned posterior being accurate pointwise in x and t and on one draw being representative.

Editorial extensions

If this is right

  • At low step counts (up to about 10 denoising steps), distributional models with λ=1 and β<2 improve FID on CIFAR-10, CelebA, LSUN Bedrooms, and latent CelebA-HQ, and raise robot-task success rates on the Libero suites, relative to classical diffusion at the same step count.
  • As the number of sampling steps grows, the optimal λ falls toward 0: the strictly-proper distributional loss (λ=1, β<2) accumulates sampling noise and underperforms, while intermediate λ still matches or beats the classical model.
  • Even with λ=0, choosing β<2 (a fractional-power distance instead of squared error) matches or slightly beats the classical regression loss, suggesting the squared-error target itself is not optimal.
  • Kernel scoring rules based on inverse-multiquadratic and RBF kernels reproduce the energy-score behavior, so the method is not tied to the specific choice of distance.
  • Trained from scratch without a teacher, the method is competitive with multi-step distillation at 8 or more function evaluations and beats DPM-solver++ beyond 8 evaluations, while requiring no distillation stage.

Reading between the lines

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

  • I would expect the single-sample plug-in in Algorithm 2 to be the first thing to improve: drawing several ξ per reverse step and averaging the resulting Gaussian conditionals gives a multi-sample estimate of p(x_s|x_t) whose variance the paper's own SNR analysis predicts to fall with m, at roughly linear extra sampling cost.
  • The empirical pattern that optimal β decreases with fewer steps suggests a time-dependent schedule — small β early in the reverse process, β→2 late — might dominate any fixed (λ, β) sweep, and is directly testable on the paper's benchmarks.
  • Because the method needs no teacher, stacking it under distillation should compound: the student would be trained on transitions that already carry posterior spread rather than on Dirac approximations, potentially removing the distillation step's usual reliance on many teacher steps.
  • The exponential kernel works despite failing the paper's diffusion-compatibility condition, so that condition is evidently sufficient but not necessary; if so, the search space for useful scoring rules is wider than the paper's theory covers.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper proposes Distributional Diffusion Models, a modification of DDIM-style diffusion training in which the conditional-mean denoiser is replaced by a generative network x̂θ(t, xt, ξ) trained with a generalized energy score or, alternatively, with kernel scoring rules (IMQ, RBF, exponential). The loss interpolates between the classical diffusion regression loss (λ→0, β→2) and a strictly proper conditional energy score (λ=1, β<2). At sampling time (Algorithm 2), each coarse reverse step draws one sample from the learned pθ_{0|t}(·|xt) and plugs it into the Gaussian conditional p(xs|x0, xt) of Eq. (4), thereby approximating the intractable integral in Eq. (5). The theory comprises a closed-form analysis of the Gaussian case under the generalized energy score (Prop 4.1), a signal-to-noise comparison of conditional versus joint scoring rules (Prop 4.2), and a diffusion-compatibility result for IMQ and RBF kernels (Prop 4.3). Experiments cover a 2D Gaussian mixture, conditional and unconditional image generation (CIFAR-10, CelebA, LSUN Bedrooms, latent CelebA-HQ), and the Libero robot-manipulation benchmark, with comparisons against DDIM-style diffusion, DPM-Solver++, and moment-matching distillation. The central claims are that distributional models outperform classical diffusion models at small numbers of sampling steps and that λ<1 trades variance fidelity against sample quality at larger step counts.

Significance. If the claims hold, the main contribution is a simple, non-adversarial training objective that unifies the standard diffusion loss and a distributional loss, with consistent few-step FID improvements in the 8-15 NFE range across all four image benchmarks (e.g., CIFAR-10 conditional: 3.21 vs 7.53 at NFE=8; latent CelebA-HQ: 8.15 vs 11.89 at NFE=10), and analogous gains on the Libero robotics suites at 2-16 steps. Strengths worth crediting: the appendix contains full proofs of the propositions; Proposition 4.1 yields a closed-form, parameter-free variance factor f(λ,β) whose predicted covariance evolution is verified in Figure 1; the experimental documentation is unusually complete (pseudocode in Appendix G, architecture and sweep details in Appendix I, hardware cost table in Section J); and the paper reports an honest failure on ImageNet 64x64 (Section K.2) as well as an explicit attribution of a related idea to a personal communication.

major comments (3)
  1. [Abstract; Section 6.2 ('Main takeaways'); Tables 4-5 in Section K.3] The abstract's claim that the method 'consistently outperform[s] standard diffusion models at few discretization steps' is contradicted by the paper's own results at the coarsest step counts. In Table 4 (CelebA, conditional), the Distributional FID at NFE=2 is 81.79 versus 62.85 for the Diffusion baseline, and in Table 5 (LSUN Bedrooms, unconditional), the Distributional FID at NFE=4 is 69.90 versus 41.57. The 'consistently outperform' statement is defensible only for NFE in the range 8-15, where the advantage holds on all four benchmarks (e.g., CIFAR-10: 3.21 vs 7.53 at NFE=8; latent CelebA-HQ: 8.15 vs 11.89 at NFE=10). The abstract and the 'Main takeaways' paragraph of Section 6.2 need to be reworded to state the regime of the improvement and to acknowledge the NFE=2 and NFE=4 exceptions.
  2. [Section 3 (Eq. (5), Algorithm 2); Section 4.1; Section 6.1 (Figures 3-4)] The paper's central mechanistic claim, namely that coarse-step sampling works because x̂θ(t, xt, ξ) faithfully approximates the posterior p_{0|t} and because a single draw from it is an adequate substitute for the integral in Eq. (5), is validated only in the 2D Gaussian-mixture experiment (Figures 3 and 4). Algorithm 2 replaces the integral in Eq. (5) with one Monte Carlo draw from pθ_{0|t}, and no error bound is provided for this plug-in when the posterior is non-Gaussian, nor for error accumulation over a multi-step coarse chain; Proposition 4.1 and Proposition C.7 cover only the Gaussian-target/Gaussian-learner case. Two confounds make the image and robotics results uninformative about the mechanism: the distributional generator has additional noise channels relative to the standard denoiser, and Algorithm 2 samples a fresh ξ at every reverse step, so the sampler is stochastic even when the churn parameter is ε=0. The β=2, λ=0 control curves in Figures 5 and 6 control for the architecture but not for the ξ-sampling effect or for posterior fidelity. I recommend a targeted test of the mechanism in a non-toy setting, for example comparing statistics of x̂θ(t, xt, ·) against a reference posterior estimate on held-out noisy latent codes, or ablating the per-step ξ resampling.
  3. [Section 6.2; Figure 7; Appendix I.2] The comparison protocol selects distributional hyperparameters on the evaluation metric, which makes the reported curves an optimistic envelope rather than a fixed model. Section 6.2 states that for the 'β<2' curves, 'we select a parameter β given one fixed λ which minimizes the FID,' and Figure 7 reports the pair (λ, β) that minimizes FID separately for each number of diffusion steps; checkpoints are likewise chosen by FID on a 2048-sample subset (Appendix I.2). The Diffusion baseline is a single fixed model, so the main comparison pits one baseline against a per-step oracle-selected family. This matters because the gains at NFE=8-15 are of the same order as the sensitivity to (λ, β): the CIFAR-10 grid at 10 steps spans FIDs from 3.6 to 7.7 (Figure 10), an interval that comfortably contains the diffusion baseline's 5.67. The detailed heatmaps in Section K.2 partially mitigate this, but the main-text curves and the abstract claim still inherit the selection. I ask the authors to report at least one curve with a fixed (λ, β) per dataset and to disclose how the entries of Tables 3-6 were selected, per NFE or per dataset.
minor comments (5)
  1. [Appendix E, Proposition E.1] The proof of Proposition E.1 states the intermediate limit lim_{n→∞} [2c_n^{1/2} − 2c_n(‖x−x′‖² + c_n)^{−1/2}] = ‖x−x′‖² and concludes f(c) = 2c for the inverse multiquadratic kernel, but the displayed expression actually tends to 0 as c_n → ∞; the correct compatible rescaling is f(c) = 2c^{3/2}, and for the RBF kernel the proof's own limit uses 2c_n² so the conclusion 'f(c) = 2c' should read f(c) = 2c². Proposition 4.3 in the main text asserts only existence of such an f, so the qualitative claim survives, but the appendix's explicit constants are wrong and need correction.
  2. [Appendix C, Lemma C.2 and Proposition C.1] Lemma C.2's proof states that fβ(c) = E‖X−c‖^β is 'strictly concave' for β∈(0,1) and concludes that lim_{t→∞} fβ(tc⋆) = −∞. Neither statement is correct on R^d for d≥2: the radial function ‖x‖^β is not concave there, and fβ grows like ‖c‖^β. The claimed minimizer property (0 is a minimizer for symmetric Gaussian X) is plausible but requires a different argument, so the proof of Proposition C.1's μ⋆=μ conclusion rests on an invalid step. In addition, the statement of Proposition C.1 writes σ⋆ = (2λ^{−2/(2−β)} − 1)^{−1}σ² where the derivation gives σ²⋆, a dimensional slip.
  3. [Section K.2, inverse-multiquadratic paragraph] The paragraph following Figure 16 states that 'when number of diffusion steps increases, the region with the best FIDs moves from λ≈0 to λ≈1,' but the heatmap in Figure 16 and the corresponding sentence in the exponential-kernel paragraph state the opposite, namely that the best λ decreases as the step count grows, consistent with Figure 7. The sentence appears to have the trend reversed and should be corrected.
  4. [Appendix I.1; Section K.2] Two documentation issues: (i) Appendix I.1 refers to 'Figure 2, right' for the squared-MMD evaluation, but Figure 2 displays the SNR comparison of Section 4.2 and the MMD panel is Figure 3; (ii) Section K.2 reports that experiments on ImageNet 64×64 'were unable to obtain satisfactory results' and defers scaling to follow-up work, an honest and important limitation that should appear in the main text or Discussion since it qualifies the generality of the method beyond the datasets tested.
  5. [Figures 5-6, 9, 19; Tables 3-6] The main FID and success-rate curves are shown without error bars, and Tables 3-6 report only 3-seed means with no standard deviations, even where adjacent entries differ by less than 0.3 FID units (e.g., CIFAR-10 at NFE=8: 3.21 vs 3.13 for Distributional vs Distillation). Reporting dispersion would materially help the reader assess the significance of the headline few-step comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

The derivation is self-contained; the loss, theory, and experiments stand independently, with no circular reduction.

full rationale

The paper's central derivation chain is not circular. The training loss (13) is a conditional generalized energy score built from known proper scoring rules, and the theoretical results (Prop. 4.1, 4.2, 4.3) are proven from explicit assumptions (Gaussian target, U-statistics asymptotics, kernel Taylor expansions) rather than from the empirical outcomes. The sampling procedure (Alg. 2) exactly plugs the learned conditional distribution into the DDIM posterior conditional in Eq. (4)-(5), and the mean/variance updates are independently derived in Appendix F from an SDE perspective. No fitted parameter is renamed as a prediction: the choice of λ and β per dataset and step count is standard hyperparameter selection on a validation FID subset, and the claim that low-step distributional models with λ=1, β<2 outperform diffusion models is an empirical result that could have failed. Self-citations, such as Shi et al. (2024) for a standard marginal-preservation property and Galashov et al. (2025) as related work, are auxiliary and not load-bearing for the main claims. The admitted ImageNet scaling limitation is an honest reporting of a negative result and does not indicate that any derivation reduces to its inputs. Overall, the paper's theoretical claims stand independently of its experiments, and the experiments are externally benchmarked against FID and task success rates, so no significant circularity is present.

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

The paper introduces no new physical or conceptual entities beyond the existing churn parameter epsilon, a reparameterization of DDIM stochasticity. No new forces, particles, or conserved quantities are postulated, so the invented-entity ledger is empty.

free parameters (5)
  • lambda (score trade-off) = 0, 0.1, 0.5, or 1.0, selected per dataset and step count
    Controls the balance between diversity and accuracy; Figure 7 shows the best lambda decreases as the number of sampling steps increases.
  • beta (energy distance exponent) = 0.0001 to 2.0, selected per dataset and step count
    Controls the sensitivity of the energy score; small beta works best at few steps in unconditional tasks.
  • loss weighting bias b = one of -2, -1, 0, 1, 2
    Sigmoid weighting over time is swept during training.
  • churn parameter epsilon = swept in {0, 0.25, 0.5, 0.75, 1.0}
    Sampler stochasticity in Algorithm 2; not part of training but affects FID.
  • population size m = 4 for images, 16 for robotics
    Number of posterior samples in the empirical loss; larger m improved images slightly but raised cost.
assumptions (5)
  • domain assumption The forward process satisfies X_t = alpha_t X_0 + sigma_t Z with alpha_0 = sigma_1 = 1 and alpha_1 = sigma_0 = 0 (Eq. 2).
    Standard interpolation that defines noise levels; all posterior formulas depend on it.
  • domain assumption The transition p(x_s|x_0,x_t) is Gaussian with the mean and covariance given in Eq. (4).
    Derived in Appendix F from a specific SDE; Algorithm 2 uses this transition.
  • ad hoc to paper A single Monte Carlo draw from p_theta_{0|t} per reverse step is a sufficiently accurate estimate of the integral in Eq. (5).
    No theoretical error bound is given for non-Gaussian targets; the paper relies on empirical validation.
  • domain assumption The network x_hat_theta(t, x_t, xi), with xi concatenated as extra channels, can represent the true posterior p_{0|t} well.
    Acknowledged in Section 7 as a limitation and a direction for future architecture work.
  • domain assumption FID is an appropriate measure of sample quality for the comparisons.
    Standard metric, but it can be insensitive to certain distributional errors.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Distributional Diffusion Models with Scoring Rules." pith.science (2026). https://pith.science/paper/KT6DH7YV

@misc{pith2026250202483,
  author       = {Pith},
  title        = {Pith review of: Distributional Diffusion Models with Scoring Rules},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KT6DH7YV}},
  note         = {Machine review of arXiv:2502.02483}
}
read the original abstract

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises" a Gaussian sample into a sample from the data distribution. However, generating high-quality outputs requires many discretization steps to obtain a faithful approximation of the reverse process. This is expensive and has motivated the development of many acceleration methods. We propose to accomplish sample generation by learning the posterior {\em distribution} of clean data samples given their noisy versions, instead of only the mean of this distribution. This allows us to sample from the probability transitions of the reverse process on a coarse time scale, significantly accelerating inference with minimal degradation of the quality of the output. This is accomplished by replacing the standard regression loss used to estimate conditional means with a scoring rule. We validate our method on image and robot trajectory generation, where we consistently outperform standard diffusion models at few discretization steps.

Figures

Figures reproduced from arXiv: 2502.02483 by the authors.

Figure 1
Figure 1. Left: variance reduction factor f(λ, β) as a function of β ∈ [0, 2] and λ ∈ [0, 1]. Right: evolution of the covariance during the sampling of distributional diffusion model for a Gaus￾sian target p0 = N (0, 4Id) with a number of denoising steps N ∈ {5, 10, . . . , 95, 100}, λ = 0.5, β = 0.2. As N increases (the color changes from blue to red), the output variance gets closer to 4. In Section 4, we discuss an alterna… view at source ↗
Figure 2
Figure 2. SNR(In) (red) and SNR(In,joint) (blue) w.r.t. σ 2 (x￾axis) for 3 possible bias levels b ∈ {0, 1, 2} (from dark to light). Vertically, we plot (σ ⋆ b ) 2 such that for the bias b, we have SNR(In) ≥ SNR(In,joint) for σ ≥ σ ⋆ b . In practice, we consider the sigmoid weighting scheme wt = (1 + exp[b − log(α 2 t /σ2 t )])−1 (Kingma et al., 2021; Hoogeboom et al., 2023), where b ∈ R is some bias. The SNR of U, V can easil… view at source ↗
Figure 3
Figure 3. Left: Squared MMD between target distribution and sampled data according to different models, x-axis denotes the number of sampling steps. Right: average standard deviation of samples X0|Xt produced by either true posterior distribution p0|t or the models xˆθ(t, Xt, ξ), x-axis is the timestep t. 5. Related Work Accelerated diffusion models. Many strategies acceler￾ate diffusion models, broadly classifiable as distil… view at source ↗
Figures from the paper (23 more)
Figure 5
Figure 5. Figure 5: Conditional image generation. x-axis denotes number of denoising steps, y-axis represents FID. Black dashed line denotes the performance of diffusion model at 100 steps. 10 30 50 70 90 100 Num diffusion steps 3 4 5 6 7 8 9 10 11 FID LSUN Bedrooms 10 30 50 70 90 100 Num…
Figure 6
Figure 6. Figure 6: Unconditional image generation. x-axis denotes num￾ber of denoising steps, y-axis represents FID. Black dashed line denotes the performance of the diffusion model at 100 steps. CelebA-HQ (256x256x3) producing latent codes of shape 64x64x3, which are then used to build …
Figure 8
Figure 8. Figure 8: Conditional generation on CIFAR-10 with different ker￾nels. x-axis is the number of diffusion steps. y-axis is the FID. Using different kernels. As discussed in Section 2.2 and in Section 3, we can also use the kernel diffusion loss. We train xˆθ with kernels (9a), (9b…
Figure 9
Figure 9. Figure 9: Performance in Libero10 as function of diffusion steps and λ. We plot the maximum success rate from best checkpoint during training. λ = 0 works best when more diffusion steps are used, and λ > 0 gives best results when fewest diffusion steps are used. λ > 0 also reduc…
Figure 10
Figure 10. Figure 10: Heatmap of FIDs for conditional image generation on CIFAR-10. x-axis corresponds to λ, y-axis corresponds to β, the color corresponds to FID going from minimal (blue) to maximal (red) values. Different columns denote number of diffusion steps. Black squares correspond…
Figure 11
Figure 11. Figure 11: Heatmap of FIDs for conditional image generation on CelebA. x-axis corresponds to λ, y-axis corresponds to β, the color corresponds to FID going from minimal (blue) to maximal (red) values. Different columns denote number of diffusion steps. Black squares correspond t…
Figure 12
Figure 12. Figure 12: Heatmap of FIDs for unconditional image generation on LSUN Bedrooms. x-axis corresponds to λ, y-axis corresponds to β, the color corresponds to FID going from minimal (blue) to maximal (red) values. Different columns denote number of diffusion steps. Black squares cor…
Figure 13
Figure 13. Figure 13: Heatmap of FIDs for unconditional image generation on Latent CelebA-HQ. x-axis corresponds to λ, y-axis corresponds to β, the color corresponds to FID going from minimal (blue) to maximal (red) values. Different columns denote number of diffusion steps. Black squares …
Figure 14
Figure 14. Figure 14: Best parameters λ and corresponding kernel parameters for each kernel, achieving the lowest FID for the given number of diffusion steps. 37 [PITH_FULL_IMAGE:figures/full_fig_p037_14.png]
Figure 15
Figure 15. Figure 15: Performance of different kernels on conditional image generation on CIFAR-10, for different values of λ (different columns). The kernel parameters are chosen to minimize FID for the given λ condition. We also report performance of the diffusion model (red) and show in…
Figure 16
Figure 16. Figure 16: Heatmap of FIDs for conditional image generation on CIFAR-10 for Inverse MQ (9a) kernel. x-axis corresponds to λ, y-axis corresponds to c, the color corresponds to FID going from minimal (blue) to maximal (red) values. Different columns denote number of diffusion step…
Figure 17
Figure 17. Figure 17: Heatmap of FIDs for conditional image generation on CIFAR-10 for RBF (9b) kernel. x-axis corresponds to λ, y-axis corresponds to σ 2 , the color corresponds to FID going from minimal (blue) to maximal (red) values. Different columns denote number of diffusion steps. B…
Figure 18
Figure 18. Figure 18: Heatmap of FIDs for conditional image generation on CIFAR-10 for Exponential (9c) kernel. x-axis corresponds to λ, y-axis corresponds to σ, the color corresponds to FID going from minimal (blue) to maximal (red) values. Different columns denote number of diffusion ste…
Figure 19
Figure 19. Figure 19: Performance in three other Libero suites - Libero-Goal, Libero-Spatial, and Libero-Object - as function of diffusion steps and λ with same settings as [PITH_FULL_IMAGE:figures/full_fig_p041_19.png]
Figure 20
Figure 20. Figure 20: Left. Performance in Libero10 as function of diffusion steps and λ, same as [PITH_FULL_IMAGE:figures/full_fig_p041_20.png]
Figure 21
Figure 21. Figure 21: Left, samples from distributional model trained on CIFAR-10 and sampled with 10 steps. β = 0.1, λ = 1. Right, samples from diffusion model trained on CIFAR-10 and sampled with 10 steps [PITH_FULL_IMAGE:figures/full_fig_p042_21.png]
Figure 22
Figure 22. Figure 22: Left, samples from distributional model trained on CIFAR-10 and sampled with 100 steps. β = 2, λ = 0. Right, samples from diffusion model trained on CIFAR-10 and sampled with 100 steps [PITH_FULL_IMAGE:figures/full_fig_p043_22.png]
Figure 23
Figure 23. Figure 23: Left, samples from distributional model trained on CelebA and sampled with 10 steps. β = 0.001, λ = 1. Right, samples from diffusion model trained on CelebA and sampled with 10 steps. 43 [PITH_FULL_IMAGE:figures/full_fig_p043_23.png]
Figure 24
Figure 24. Figure 24: Left, samples from distributional model trained on CelebA and sampled with 100 steps. β = 2, λ = 1. Right, samples from diffusion model trained on CelebA and sampled with 100 steps [PITH_FULL_IMAGE:figures/full_fig_p044_24.png]
Figure 25
Figure 25. Figure 25: Left, samples from distributional model trained on LSUN Bedrooms and sampled with 10 steps. β = 0.0001, λ = 1. Right, samples from diffusion model trained on LSUN Bedrooms and sampled with 10 steps 44 [PITH_FULL_IMAGE:figures/full_fig_p044_25.png]
Figure 26
Figure 26. Figure 26: Left, samples from distributional model trained on LSUN Bedrooms and sampled with 100 steps. β = 0.0001, λ = 0. Right, samples from diffusion model trained on LSUN Bedrooms and sampled with 100 steps [PITH_FULL_IMAGE:figures/full_fig_p045_26.png]
Figure 27
Figure 27. Figure 27: Left, samples from distributional model trained on latent CelebA HQ and sampled with 10 steps. β = 0.01, λ = 0.5. Right, samples from diffusion model trained on latent CelebA HQ and sampled with 10 steps. 45 [PITH_FULL_IMAGE:figures/full_fig_p045_27.png]
Figure 28
Figure 28. Figure 28: Left, samples from distributional model trained on latent CelebA HQ and sampled with 100 steps. β = 0.01, λ = 0.1. Right, samples from diffusion model trained on latent CelebA HQ and sampled with 100 steps. 46 [PITH_FULL_IMAGE:figures/full_fig_p046_28.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Generative Modeling via Kernelized Stochastic Interpolants

    cs.LG 2026-02 conditional novelty 6.0 of 10

    The drift of a stochastic interpolant is estimated by solving a P×P linear system from feature gradients, enabling training-free generation and training-free combination of pretrained generative models.

Reference graph

Works this paper leans on

86 extracted references · 57 canonical work pages · cited by 1 Pith paper

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

  2. [2]

    Fast inference in denoising diffusion models via MMD finetuning

    Aiello, E., Valsesia, D., and Magli, E. Fast inference in denoising diffusion models via MMD finetuning. IEEE Access, 12: 0 106912--106923, 2024. doi:10.1109/ACCESS.2024.3436698

    work page arXiv 2024

  3. [3]

    S., Boffi, N

    Albergo, M. S., Boffi, N. M., and Vanden-Eijnden, E. Stochastic interpolants: A unifying framework for flows and diffusions. arXiv preprint arXiv:2303.08797, 2023

    arXiv 2023

  4. [4]

    Estimating the optimal covariance with imperfect mean in diffusion probabilistic models

    Bao, F., Li, C., Sun, J., Zhu, J., and Zhang, B. Estimating the optimal covariance with imperfect mean in diffusion probabilistic models. In International Conference on Machine Learning, 2022 a

    2022

  5. [5]

    Analytic- DPM : an analytic estimate of the optimal reverse variance in diffusion probabilistic models

    Bao, F., Li, C., Zhu, J., and Zhang, B. Analytic- DPM : an analytic estimate of the optimal reverse variance in diffusion probabilistic models. In International Conference on Learning Representations, 2022 b

    2022

  6. [6]

    G., Danihelka, I., Dabney, W., Mohamed, S., Lakshminarayanan, B., Hoyer, S., and Munos, R

    Bellemare, M. G., Danihelka, I., Dabney, W., Mohamed, S., Lakshminarayanan, B., Hoyer, S., and Munos, R. The C ramer distance as a solution to biased W asserstein gradients. arXiv preprint arXiv:1705.10743, 2017

    arXiv 2017

  7. [7]

    and Thomas-Agnan , C

    Berlinet, A. and Thomas-Agnan , C. Reproducing Kernel Hilbert Spaces in Probability and Statistics. Kluwer, 2004

    2004

  8. [8]

    J., Arbel, M., and Gretton, A

    Bi \'n kowski, M., Sutherland, D. J., Arbel, M., and Gretton, A. Demystifying MMD GAN s. In International Conference on Learning Representations, 2018

    2018

Show all 86 references
  1. [9]

    K., and Nowozin, S

    Bouchacourt, D., Mudigonda, P. K., and Nowozin, S. Disco nets: Dissimilarity coefficients networks. In Advances in Neural Information Processing Systems, 2016

    2016

  2. [10]

    Chen, H., Ren, Y., Ying, L., and Rotskoff, G. M. Accelerating diffusion models with parallel sampling: Inference at sub-linear time complexity. In Advances in Neural Information Processing Systems, 2024 a

    2024

  3. [11]

    Generative machine learning methods for multivariate ensemble postprocessing

    Chen, J., Janke, T., Steinke, F., and Lerch, S. Generative machine learning methods for multivariate ensemble postprocessing. The Annals of Applied Statistics, 18 0 (1): 0 159--183, 2024 b

    2024

  4. [12]

    J., Norouzi, M., and Chan, W

    Chen, N., Zhang, Y., Zen, H., Weiss, R. J., Norouzi, M., and Chan, W. WaveGrad : Estimating gradients for waveform generation. In International Conference on Learning Representations, 2021

    2021

  5. [13]

    Conditional GAN for enhancing diffusion models in efficient and authentic global gesture generation from audios

    Cheng, Y., Liang, M., Huang, S., Han, G., Ning, J., and Liu, W. Conditional GAN for enhancing diffusion models in efficient and authentic global gesture generation from audios. arXiv preprint arXiv:2410.20359, 2024

    2024 arXiv

  6. [14]

    Diffusion policy: Visuomotor policy learning via action diffusion

    Chi, C., Xu, Z., Feng, S., Cousineau, E., Du, Y., Burchfiel, B., Tedrake, R., and Song, S. Diffusion policy: Visuomotor policy learning via action diffusion. International Journal of Robotics Research, 2023

    2023

  7. [15]

    BERT :pre-training of deep bidirectional transformers for language understanding

    Devlin, J., Chang, M.-W., Lee, K., and Toutanova, K. BERT :pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018

    2018 arXiv

  8. [16]

    The paradox of diffusion distillation, 2024

    Dieleman, S. The paradox of diffusion distillation, 2024. URL https://sander.ai/2024/02/28/paradox.html

    2024

  9. [17]

    K., Roy, D

    Dziugaite, G. K., Roy, D. M., and Ghahramani, Z. Training generative neural networks via maximum mean discrepancy optimization. In Uncertainty in Artificial Intelligence, 2015

    2015

  10. [18]

    Unifying GAN s and score-based diffusion as generative particle models

    Franceschi, J.-Y., Gartrell, M., Dos Santos, L., Issenhuth, T., de B \'e zenac, E., Chen, M., and Rakotomamonjy, A. Unifying GAN s and score-based diffusion as generative particle models. Advances in Neural Information Processing Systems, 2024

    2024

  11. [19]

    Fukumizu, K., Gretton, A., Sch\" o lkopf, B., and Sriperumbudur, B. K. Characteristic kernels on groups and semigroups. In Advances in Neural Information Processing Systems, 2008

    2008

  12. [20]

    Deep MMD gradient flow without adversarial training

    Galashov, A., de Bortoli, V., and Gretton, A. Deep MMD gradient flow without adversarial training. In International Conference on Learning Representations, 2025

    2025

  13. [21]

    D., Murphy, K

    Gao, R., Hoogeboom, E., Heek, J., Bortoli, V. D., Murphy, K. P., and Salimans, T. Diffusion meets flow matching: Two sides of the same coin. 2024. URL https://diffusionflow.github.io/

    2024

  14. [22]

    and Raftery, A

    Gneiting, T. and Raftery, A. E. Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association, 102 0 (477): 0 359--378, 2007

    2007

  15. [23]

    Generative adversarial nets

    Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. Generative adversarial nets. Advances in Neural Information Processing Systems, 2014

    2014

  16. [24]

    Introduction to RKHS , and some simple kernel algorithms

    Gretton, A. Introduction to RKHS , and some simple kernel algorithms. Advanced Topics in Machine Learning lecture, University College London, 2013

    2013

  17. [25]

    M., Rasch, M

    Gretton, A., Borgwardt, K. M., Rasch, M. J., Sch \"o lkopf, B., and Smola, A. A kernel two-sample test. Journal of Machine Learning Research, 13 0 (1): 0 723--773, 2012

    2012

  18. [26]

    A spectral energy distance for parallel speech synthesis

    Gritsenko, A., Salimans, T., van den Berg, R., Snoek, J., and Kalchbrenner, N. A spectral energy distance for parallel speech synthesis. In Advances in Neural Information Processing Systems, 2020

    2020

  19. [27]

    Deep residual learning for image recognition

    He, K., Zhang, X., Ren, S., and Sun, J. Deep residual learning for image recognition. In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, 2016

    2016

  20. [28]

    GAN s trained by a two time-scale update rule converge to a local N ash equilibrium

    Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., and Hochreiter, S. GAN s trained by a two time-scale update rule converge to a local N ash equilibrium. In Advances in Neural Information Processing Systems, 2017

    2017

  21. [29]

    Denoising diffusion probabilistic models

    Ho, J., Jain, A., and Abbeel, P. Denoising diffusion probabilistic models. In Advances in Neural Information Processing Systems, 2020

    2020

  22. [30]

    Ho, J., Salimans, T., Gritsenko, A., Chan, W., Norouzi, M., and Fleet, D. J. Video diffusion models. In Advances in Neural Information Processing Systems, 2022

    2022

  23. [31]

    simple diffusion: End-to-end diffusion for high resolution images

    Hoogeboom, E., Heek, J., and Salimans, T. simple diffusion: End-to-end diffusion for high resolution images. In International Conference on Machine Learning, 2023

    2023

  24. [32]

    Flow generator matching

    Huang, Z., Geng, Z., Luo, W., and Qi, G.-j. Flow generator matching. arXiv preprint arXiv:2410.19310, 2024

    2024 arXiv

  25. [33]

    Hutchinson, M. F. A stochastic estimator of the trace of the influence matrix for L aplacian smoothing splines. Communications in Statistics-Simulation and Computation, 18 0 (3): 0 1059--1076, 1989

    1989

  26. [34]

    Non-adversarial training of neural SDE s with signature kernel scores

    Issa, Z., Horvath, B., Lemercier, M., and Salvi, C. Non-adversarial training of neural SDE s with signature kernel scores. In Advances in Neural Information Processing Systems, 2024

    2024

  27. [35]

    Gotta go fast when generating data with score-based models

    Jolicoeur-Martineau, A., Li, K., Pich \'e -Taillefer, R., Kachman, T., and Mitliagkas, I. Gotta go fast when generating data with score-based models. arXiv preprint arXiv:2105.14080, 2021

    2021 arXiv

  28. [36]

    Elucidating the design space of diffusion-based generative models

    Karras, T., Aittala, M., Aila, T., and Laine, S. Elucidating the design space of diffusion-based generative models. In Advances in Neural Information Processing Systems, 2022

    2022

  29. [37]

    Variational diffusion models

    Kingma, D., Salimans, T., Poole, B., and Ho, J. Variational diffusion models. Advances in Neural Information Processing Systems, 2021

    2021

  30. [38]

    Mmd gan: Towards deeper understanding of moment matching network

    Li, C.-L., Chang, W.-C., Cheng, Y., Yang, Y., and Poczos, B. Mmd gan: Towards deeper understanding of moment matching network. In Advances in Neural Information Processing Systems, 2017

    2017

  31. [39]

    Generative moment matching networks

    Li, Y., Swersky, K., and Zemel, R. Generative moment matching networks. In International Conference on Machine Learning, 2015

    2015

  32. [40]

    T., Ben-Hamu, H., Nickel, M., and Le, M

    Lipman, Y., Chen, R. T., Ben-Hamu, H., Nickel, M., and Le, M. Flow matching for generative modeling. In International Conference on Learning Representations, 2023

    2023

  33. [41]

    Libero: Benchmarking knowledge transfer for lifelong robot learning

    Liu, B., Zhu, Y., Gao, C., Feng, Y., Liu, Q., Zhu, Y., and Stone, P. Libero: Benchmarking knowledge transfer for lifelong robot learning. In Advances in Neural Information Processing Systems, 2024

    2024

  34. [42]

    On the two-sample statistic approach to generative adversarial networks

    Liu, L. On the two-sample statistic approach to generative adversarial networks. Master's thesis, University of Princeton Senior Thesis, April 2017. URL http://arks.princeton.edu/ark:/88435/dsp0179408079v

    2017

  35. [43]

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

    Liu, X., Gong, C., et al. Flow straight and fast: Learning to generate and transfer data with rectified flow. In International Conference on Learning Representations, 2023

    2023

  36. [44]

    DPM -solver++: Fast solver for guided sampling of diffusion probabilistic models

    Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J. DPM -solver++: Fast solver for guided sampling of diffusion probabilistic models. arXiv preprint arXiv:2211.01095, 2022

    2022 arXiv

  37. [45]

    and Luhman, T

    Luhman, E. and Luhman, T. Knowledge distillation in iterative generative models for improved sampling speed. arXiv preprint arXiv:2101.02388, 2021

    2021 arXiv

  38. [46]

    A comprehensive survey on knowledge distillation of diffusion models

    Luo, W. A comprehensive survey on knowledge distillation of diffusion models. arXiv preprint arXiv:2304.04262, 2023

    2023 arXiv

  39. [47]

    On distillation of guided diffusion models

    Meng, C., Rombach, R., Gao, R., Kingma, D., Ermon, S., Ho, J., and Salimans, T. On distillation of guided diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023

    2023

  40. [48]

    Nichol, A. Q. and Dhariwal, P. Improved denoising diffusion probabilistic models. In International Conference on Machine Learning, 2021

    2021

  41. [49]

    Z., Li, Y., and Barber, D

    Ou, Z., Zhang, M., Zhang, A., Xiao, T. Z., Li, Y., and Barber, D. Diffusion model with optimal covariance matching. arXiv preprint arXiv:2406.10808, 2024

    2024 arXiv

  42. [50]

    A., Dueben, P., and Dutta, R

    Pacchiardi, L., Adewoyin, R. A., Dueben, P., and Dutta, R. Probabilistic forecasting with generative networks via scoring rule minimization. Journal of Machine Learning Research, 25 0 (45): 0 1--64, 2024

    2024

  43. [51]

    T., and Mildenhall, B

    Poole, B., Jain, A., Barron, J. T., and Mildenhall, B. Dreamfusion: Text-to-3d using 2d diffusion. In International Conference on Learning Representations, 2023

    2023

  44. [52]

    Rizzo, M. L. and Sz \'e kely, G. J. Energy distance. Wiley Interdisciplinary Reviews: Computational Statistics, 8 0 (1): 0 27--38, 2016

    2016

  45. [53]

    High-resolution image synthesis with latent diffusion models

    Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on Computer Vision and Pattern Recognition, 2022

    2022

  46. [54]

    U-net: Convolutional networks for biomedical image segmentation

    Ronneberger, O., Fischer, P., and Brox, T. U-net: Convolutional networks for biomedical image segmentation. In Medical image computing and computer-assisted intervention--MICCAI 2015: 18th international conference, Munich, Germany, October 5-9, 2015, proceedings, part III 18, ...

    2015

  47. [55]

    Learning diffusion priors from observations by expectation maximization

    Rozet, F., Andry, G., Lanusse, F., and Louppe, G. Learning diffusion priors from observations by expectation maximization. In Advances in Neural Information Processing Systems, 2024

    2024

  48. [56]

    C., and Fei-Fei, L

    Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., Berg, A. C., and Fei-Fei, L. ImageNet Large Scale Visual Recognition Challenge . International Journal of Computer Vision (IJCV), 115 0 (3): 0 211--252, 201...

    2015 doi

  49. [57]

    Palette: Image-to-image diffusion models

    Saharia, C., Chan, W., Chang, H., Lee, C., Ho, J., Salimans, T., Fleet, D., and Norouzi, M. Palette: Image-to-image diffusion models. In ACM SIGGRAPH, 2022 a

    2022

  50. [58]

    L., Ghasemipour, K., Gontijo Lopes, R., Karagol Ayan, B., and Salimans, T

    Saharia, C., Chan, W., Saxena, S., Li, L., Whang, J., Denton, E. L., Ghasemipour, K., Gontijo Lopes, R., Karagol Ayan, B., and Salimans, T. Photorealistic text-to-image diffusion models with deep language understanding. Advances in Neural Information Processing Systems, 2022 b

    2022

  51. [59]

    and Ho, J

    Salimans, T. and Ho, J. Progressive distillation for fast sampling of diffusion models. In International Conference on Learning Representations, 2022

    2022

  52. [60]

    Improving GAN s using optimal transport

    Salimans, T., Zhang, H., Radford, A., and Metaxas, D. Improving GAN s using optimal transport. In International Conference on Learning Representations, 2018

    2018

  53. [61]

    Multistep distillation of diffusion models via moment matching

    Salimans, T., Mensink, T., Heek, J., and Hoogeboom, E. Multistep distillation of diffusion models via moment matching. In Advances in Neural Information Processing Systems, 2024

    2024

  54. [62]

    Adversarial diffusion distillation

    Sauer, A., Lorenz, D., Blattmann, A., and Rombach, R. Adversarial diffusion distillation. In European Conference on Computer Vision, pp.\ 87--103. Springer, 2025

    2025

  55. [63]

    Equivalence of distance-based and RKHS -based statistics in hypothesis testing

    Sejdinovic, D., Sriperumbudur, B., Gretton, A., and Fukumizu, K. Equivalence of distance-based and RKHS -based statistics in hypothesis testing. The Annals of Statistics, pp.\ 2263--2291, 2013

    2013

  56. [64]

    Serfling, R. J. Approximation Theorems of Mathematical Statistics. John Wiley & Sons, 2009

    2009

  57. [65]

    and Meinshausen, N

    Shen, X. and Meinshausen, N. Engression: extrapolation through the lens of distributional regression. Journal of the Royal Statistical Society Series B: Statistical Methodology, 2024

    2024

  58. [66]

    Reverse M arkov learning: Multi-step generative models for complex distributions

    Shen, X., Meinshausen, N., and Zhang, T. Reverse M arkov learning: Multi-step generative models for complex distributions. arXiv preprint arXiv:2502.13747, 2025

    2025 arXiv

  59. [67]

    Diffusion S chr \"o dinger bridge matching

    Shi, Y., De Bortoli, V., Campbell, A., and Doucet, A. Diffusion S chr \"o dinger bridge matching. In Advances in Neural Information Processing Systems, 2024

    2024

  60. [68]

    Parallel sampling of diffusion models

    Shih, A., Belkhale, S., Ermon, S., Sadigh, D., and Anari, N. Parallel sampling of diffusion models. In Advances in Neural Information Processing Systems, 2023

    2023

  61. [69]

    S., Schiff, Y., and Kuleshov, V

    Si, P., Chen, Z., Sahoo, S. S., Schiff, Y., and Kuleshov, V. Semi-autoregressive energy flows: exploring likelihood-free training of normalizing flows. In International Conference on Machine Learning, 2023

    2023

  62. [70]

    Deep unsupervised learning using nonequilibrium thermodynamics

    Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N., and Ganguli, S. Deep unsupervised learning using nonequilibrium thermodynamics. In International Conference on Machine Learning, 2015

    2015

  63. [71]

    Denoising diffusion implicit models

    Song, J., Meng, C., and Ermon, S. Denoising diffusion implicit models. In International Conference on Learning Representations, 2021 a

    2021

  64. [72]

    and Ermon, S

    Song, Y. and Ermon, S. Generative modeling by estimating gradients of the data distribution. In Advances in Neural Information Processing Systems, 2019

    2019

  65. [73]

    P., Kumar, A., Ermon, S., and Poole, B

    Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021 b

    2021

  66. [74]

    Consistency models

    Song, Y., Dhariwal, P., Chen, M., and Sutskever, I. Consistency models. In International Conference on Machine Learning, 2023

    2023

  67. [75]

    K., Gretton, A., Fukumizu, K., Lanckriet, G

    Sriperumbudur, B. K., Gretton, A., Fukumizu, K., Lanckriet, G. R. G., and Sch \"o lkopf, B. Hilbert space embeddings and metrics on probability measures. Journal of Machine Learning Research, 11: 0 1517--1561, 2010

    2010

  68. [76]

    K., Fukumizu, K., and Lanckriet, G

    Sriperumbudur, B. K., Fukumizu, K., and Lanckriet, G. R. G. Universality, characteristic kernels and RKHS embedding of measures. Journal of Machine Learning Research, 12: 0 2389--2410, 2011

    2011

  69. [77]

    and Christmann, A

    Steinwart, I. and Christmann, A. Support Vector Machines. Information Science and Statistics. Springer, 2008

    2008

  70. [78]

    Sz \'e kely, G. J. and Rizzo, M. L. Energy statistics: A class of statistics based on distances. Journal of Statistical Planning and Inference, 143 0 (8): 0 1249--1272, 2013

    2013

  71. [79]

    Coulomb GAN s: Provably optimal N ash equilibria via potential fields

    Unterthiner, Nessler, Seward, Klambauer, Heusel, Ramsauer, and Hochreiter. Coulomb GAN s: Provably optimal N ash equilibria via potential fields. In International Conference on Learning Representations, 2018

    2018

  72. [80]

    Neural discrete representation learning

    van den Oord, A., Vinyals, O., and Kavukcuoglu, K. Neural discrete representation learning. In Advances in Neural Information Processing Systems, 2017

    2017

  73. [81]

    N., Kondor, R., and Borgwardt, K

    Vishwanathan, S., Schraudolph, N. N., Kondor, R., and Borgwardt, K. M. Graph kernels. Journal of Machine Learning Research, 11 0 (40): 0 1201--1242, 2010

    2010

  74. [82]

    Tackling the generative learning trilemma with denoising diffusion GAN s

    Xiao, Z., Kreis, K., and Vahdat, A. Tackling the generative learning trilemma with denoising diffusion GAN s. In International Conference on Learning Representations, 2022

    2022

  75. [83]

    Xu, Y., Tong, S., and Jaakkola, T. S. Stable target field for reduced variance score estimation in diffusion models. In International Conference on Learning Representations, 2023

    2023

  76. [84]

    UFO gen: You forward once large scale text-to-image generation via diffusion GAN s

    Xu, Y., Zhao, Y., Xiao, Z., and Hou, T. UFO gen: You forward once large scale text-to-image generation via diffusion GAN s. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.\ 8196--8206, 2024

    2024

  77. [85]

    Z., Tompson, J., Driess, D., Florence, P., Ghasemipour, K., Finn, C., and Wahid, A

    Zhao, T. Z., Tompson, J., Driess, D., Florence, P., Ghasemipour, K., Finn, C., and Wahid, A. ALOHA unleashed: A simple recipe for robot dexterity. arXiv preprint arXiv:2410.13126, 2024

    2024 arXiv

  78. [86]

    DPM -solver-v3: Improved diffusion ODE solver with empirical model statistics

    Zheng, K., Lu, C., Chen, J., and Zhu, J. DPM -solver-v3: Improved diffusion ODE solver with empirical model statistics. In Advances in Neural Information Processing Systems, 2023

    2023

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.