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Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior

T0 review · 4 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Diffusion Posterior Sampling is actually maximizing a posterior, not sampling one, and a faithful MAP implementation performs better.

desk verdict A useful empirical challenge to the conditional-score story for DPS, with an honest MAP hypothesis and solid algorithmic gains; the headline evidence has a statistical hole, but the paper earns a serious read. read the letter →

arxiv 2501.18913 v2 pith:G2URZO24 submitted 2025-01-31 cs.CV

Tongda Xu , Xiyan Cai , Xinjie Zhang , Xingtong Ge , Dailan He , Ming Sun , Jingjing Liu , Ya-Qin Zhang
show 2 more authors
Jian Li Yan Wang
This is my paper · ORCID
classification cs.CV
keywords diffusionposteriorsamplingMAPestimationconditionalscoreinverseproblemsimagerestorationlatentsphereprojectionfew-shot
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that Diffusion Posterior Sampling (DPS), a popular zero-shot method for inverse problems, does not approximate the conditional score for posterior sampling as previously believed. Instead, it behaves like a MAP estimator: at each diffusion step it tries to maximize the conditional posterior $p_\theta(X_{t-1}|X_t, y)$, which yields high-quality but low-diversity samples. The authors support this with three empirical observations on 512×512 ImageNet: DPS's score estimate diverges sharply from a well-trained conditional model (StableSR) and is even worse than the unconditional score; the mean of DPS's score estimate is far from zero, which a valid score cannot have; and DPS samples show much lower per-pixel variance than StableSR. Based on this MAP interpretation, they propose DMAP, which runs multi-step gradient ascent on $\log p_\theta(y|X_{t-1})$ with projection onto the sphere where the transition distribution concentrates, and a lightweight conditional score estimator trainable on only 100 images in 8 GPU hours. Both improvements substantially outperform DPS on super-resolution, Gaussian deblurring, and non-linear deblurring at 512×512 resolution.

What carries the argument

The central machinery is the high-dimensional concentration of the conditional Gaussian transition: as dimension $d\to\infty$, the distribution $p_\theta(X_{t-1}|X_t)$ concentrates on the surface of a sphere centered at $E[X_{t-1}|X_t]$ with radius $\sqrt{d}\sigma_t$. This converts the MAP objective $\arg\max p_\theta(X_{t-1}|X_t,y)$ into a constrained optimization: maximize $\log p_\theta(y|X_{t-1})$ subject to $X_{t-1}$ lying on that sphere (Proposition 3). DMAP then alternates multiple gradient-ascent steps of $\log p_\theta(y|X_{t-1})$ with orthogonal projection onto the sphere, making it a faithful MAP solver where DPS (one gradient step, no projection) and DSG (projection, single step) are partial implementations. A second ingredient is a lightweight conditional score estimator $q_\theta(X_{t-1}|X_t,y)$—a ControlNet trained on 100 images—used only as the initialization of the constrained optimization, justified by Proposition 4 through a cross-entropy comparison with the unconditional prior.

What would settle it

Take a second, independently trained conditional score reference—for example, a pixel-space diffusion model trained on paired data for the same super-resolution task—and recompute the score-error and score-mean statistics over a large set of images. If DPS's score error is not consistently larger than the unconditional score's error, or its score mean returns near zero for the working hyperparameter setting, the MAP hypothesis loses its empirical foundation.

Watch

Extended reading notes

Core claim

On the paper's own terms: DPS is not a conditional score estimator; it is a MAP optimizer. The authors state Hypothesis 2: instead of sampling $X_{t-1} \sim p_\theta(X_{t-1}|X_t, y)$, DPS in effect computes $X_{t-1} \leftarrow \arg\max p_\theta(X_{t-1}|X_t, y)$. They support this with three observations: (I) DPS's implied score $s_{\mathrm{DPS}}(X_t,t,y) = s_\theta(X_t,t) - \frac{\sqrt{\alpha_t}}{\beta_t}\zeta_t \nabla_{X_t}\|f(E[X_0|X_t])-y\|$ deviates far more from the score of StableSR, a trained conditional super-resolution model, than the unconditional score does; (II) the mean of DPS's score estimate is about 5.8 at $\zeta_t=4.8$, versus roughly 0.4 for the unconditional and StableSR scores, violating the zero-mean property expected of any score function; and (III) DPS exhibits markedly lower per-pixel sample variance than StableSR. They then prove (Proposition 3) that in the high-dimensional limit the MAP step is equivalent to $\arg\max \log p_\theta(y|X_{t-1})$ subject to $X_{t-1} \sim p_\theta(X_{t-1}|X_t)$, because the isotropic Gaussian transition concentrates on the surface of a sphere centered at $E[X_{t-1}|X_t]$ with radius $\sqrt{d}\sigma_t$. DMAP implements this by performing $K$ steps of gradient ascent on the likelihood term and then projecting back onto that sphere. A second improvement uses a ControlNet-based conditional score estimator trained on as few as 100 images (8 GPU hours) as a better initialization for the constrained optimization, justified by Proposition 4: any approximate posterior with lower cross-entropy to the true posterior yields a higher expected $\log p_\theta(y|X_{t-1})$ than the unconditional prior. On ImageNet 512 super-resolution, Gaussian deblurring, and non-linear deblurring, DMAP and DPS+CSE improve PSNR, LPIPS, and FID over DPS and prior DPS variants.

Load-bearing premise

The empirical case that DPS's score estimate is badly wrong relies on treating StableSR's score as a trustworthy proxy for the true conditional score; if StableSR is itself far from the true conditional score, the measured divergence may just say that DPS differs from StableSR rather than from the true score.

Editorial extensions

If this is right

  • If DPS is MAP, then the sampling-based guarantees for posterior sampling (score approximation error bounds) are not the right lens for explaining DPS; the algorithm is solving an optimization problem, not approximating a sampler.
  • DMAP with two gradient steps and half the diffusion steps matches DPS's runtime while improving PSNR, LPIPS, and FID, so the MAP interpretation yields a practical algorithm that is both faster and better.
  • A conditional score estimator trained on as few as 100 images (8 GPU hours) substantially boosts DPS, and gains saturate around 1000 images or with self-generated data, indicating that very small training sets can provide useful conditioning information.
  • The MAP view explains previously puzzling observations: why Adam helps DPS (adaptive step sizes are natural for optimization), why DPS has a large score-error lower bound in high dimensions, and why DPS samples lack diversity.
  • DMAP continues to outperform DPS when the conditional score estimator is added, so the two improvements are complementary rather than redundant.

Reading between the lines

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

  • If DPS is truly a MAP estimator, then comparisons against posterior samplers should be reframed: the diversity shortfall is a feature of optimization, not a bug, and applications that require diverse solutions would need explicit diversity-encouraging mechanisms on top of DMAP.
  • The sphere-projection recipe could generalize beyond inverse problems: any guided diffusion update that pushes a sample away from the concentration sphere could benefit from an explicit projection step, a variant that could be tested on classifier guidance or classifier-free guidance.
  • The 100-image ControlNet result suggests a few-shot inverse-problem pipeline: for a new forward operator, one could fine-tune a tiny conditional score estimator on a handful of real measurements rather than relying purely on zero-shot heuristics, and the paper's Proposition 4 gives a principled condition for when this helps.
  • A natural testable extension is to measure whether DMAP's per-pixel variance goes exactly to zero in the limit of many gradient steps, which would confirm the deterministic MAP characterization and distinguish it from a sampler with low but nonzero entropy.
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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

4 major / 4 minor

Summary. The paper challenges the standard interpretation of Diffusion Posterior Sampling (DPS) as a conditional score estimator and proposes that DPS is better understood as implicitly maximizing a posterior (MAP). Three empirical observations are offered: (I) DPS's score estimate deviates more from a well-trained conditional score (StableSR) than the unconditional score does; (II) the empirical mean of DPS's score estimate is far from zero, which the authors take as evidence of invalidity; and (III) DPS samples have low diversity. Based on these observations, the authors hypothesize that DPS performs MAP estimation and introduce DMAP, a variant that performs multi-step gradient ascent with spherical projection, plus a lightweight ControlNet-based conditional score estimator (CSE) trained on 100 images in 8 GPU hours. Experiments on 512x512 ImageNet show that DMAP and DPS+CSE improve PSNR, LPIPS, and FID over DPS and several baselines across super-resolution and deblurring tasks.

Significance. If the MAP reinterpretation is correct, it would reframe how the community understands a widely used family of diffusion-based inverse problem solvers, with consequences for theory, hyperparameter choice, and algorithm design. The paper also delivers a practical algorithmic contribution: DMAP with multi-step gradient ascent and sphere projection, and a data-efficient CSE, yield consistent and sometimes large improvements across several tasks in Table 4. The authors provide source code and fairly extensive ablations, including training set size and compute time. However, the central conceptual claim rests on three observations whose statistical validity is currently incomplete; Observation II in particular is based on an invalid test. The empirical improvements are valuable regardless of the hypothesis, but the paper's main interpretive contribution needs stronger support.

major comments (4)
  1. [Section 3.3, Eq. (12), Table 2] The zero-mean identity for a valid score holds under expectation with respect to the conditional density p(X|y), i.e., E_{p(X|y)}[∇_X log p(X|y)] = 0. Table 2, however, reports means over 1000 samples of X_T drawn from the unconditional noise distribution N(0,I), which is independent of y. For a conditional score, E_{p(X_T)}[∇ log p(X_T|y)] = E_{p(X_T)}[∇ log p(y|X_T)] + E_{p(X_T)}[∇ log p(X_T)] = E_{p(X_T)}[∇ log p(y|X_T)], which is generically nonzero and can be large when the likelihood term is strongly weighted. The DPS update in Eq. (9) explicitly contains the likelihood gradient scaled by ζ_t, so the large mean for ζ_t=4.8 may simply reflect the expected likelihood gradient rather than an invalid score. The comparison with StableSR's near-zero mean is therefore not a valid test of score validity. The authors should either compute the mean under samples from p(X|y) (e.g., using a well-trained conditional model) or directly estimate the expected likelihood gradient term and subtract it before drawing conclusions.
  2. [Section 3.2, Figure 1, Appendix B.1] The quantitative score-error plot in Figure 1 is computed from a single ImageNet image (ILSVRC2012_val_00000013.png), as stated in Appendix B.1. No error bars, multiple images, or random seeds are reported, so the claim that DPS's score error is 'significantly larger' than the unconditional score is not established with any measure of variability. Additionally, the use of StableSR as the reference 'true' conditional score is an assumption; StableSR is a real-world super-resolution model, and its superiority in FID/KID/LPIPS does not logically imply that its score is closer to the true posterior score than DPS's estimate. The authors should provide score-error statistics over at least a handful of images with confidence intervals, and should discuss the limitations of using StableSR as ground truth.
  3. [Section 4.1, Algorithm 2, Proposition 3] The claim that DMAP is a 'faithful implementation' of the MAP problem in Eq. (15) is not fully supported. The gradient step in Algorithm 2 (line 6) uses ∇_{x_{t-1}} ||f(E[X0|x_{t-1}]) - y||, but E[X0|x_{t-1}] itself depends on x_{t-1} through the Tweedie formula (Eq. 4). The gradient of the composition is not equal to the gradient of log p(y|x_{t-1}) unless one ignores the Jacobian of E[X0|·] with respect to x_{t-1}. Thus the multi-step ascent is maximizing a heuristic proxy rather than the explicit posterior. The proof of Proposition 3 establishes a limiting equivalence for the constrained problem, but it does not justify replacing log p(y|X_{t-1}) with -||f(E[X0|X_{t-1}])-y||. The authors should state this approximation explicitly and, ideally, justify it or provide an ablation that uses the full Jacobian.
  4. [Section 3.5, Hypothesis 2, Section 5.2] The paper frames the MAP interpretation as a hypothesis and then uses the success of DMAP, which is built on that hypothesis, as evidence for it. This is a mild confirmation loop: the empirical gains of DMAP show that multi-step gradient ascent with projection helps, but they do not independently establish that DPS itself is a MAP estimator. The partial derivation for DSG in Appendix A.3 is a step in the right direction, but it relies on strong assumptions and does not cover DPS. To strengthen the central claim, the authors could provide a direct derivation of DPS as an approximate MAP update under explicit conditions, or compare DPS's behavior against a known MAP estimator in a controlled setting (e.g., the toy example in Appendix A.4) with quantitative agreement rather than just qualitative mode collapse.
minor comments (4)
  1. [Algorithm 3, Appendix A.1] Line 5 of Algorithm 3 (Latent DPS) writes 'x_{t-1} = x_{t-1} - ...' but should use the latent variable z_{t-1} for consistency.
  2. [Table 2 and Table 3] The value 0.3939 appears both as StableSR's score mean in Table 2 and as StableSR's per-pixel standard deviation in Table 3; this coincidence is suspicious and should be checked to rule out a copy-paste error.
  3. [Equation (8)] The text says the l2 norm is weighted by ζ_t, but Eq. (8) writes exp(-ζ_t ||f(E[X0|Xt])-y||), which is a plain l2 norm times ζ_t; the wording 'weighted l2 norm' is ambiguous.
  4. [Section 3.3] The authors state that any valid score has zero mean, but the empirical means of the unconditional score and StableSR are around 0.4, which is not particularly close to zero. A brief discussion of finite-sample effects, discretization, or the scale of typical score values would clarify why 0.4 is considered negligible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the MAP reinterpretation is an explicitly labeled hypothesis, DMAP is independently implemented and tested against external baselines, and no load-bearing step reduces to its own inputs.

full rationale

The paper does not exhibit a circular derivation chain. The central claim (Hypothesis 2) is explicitly framed as a hypothesis, not a theorem: Section 3.5 states 'we hypothesize that DPS is closer to another paradigm of image restoration other than posterior sampling: the maximization of a posterior (MAP) estimate,' and Appendix A.3 concedes 'For now, we can not derive MAP directly from DPS.' The supporting observations are empirical comparisons against external references (StableSR, ControlNet, and standard baselines DPS/PSLD/FreeDOM/ReSample/DSG), and DMAP is not obtained by fitting a parameter to the data it later 'predicts'; it is a new algorithm built from the hypothesis and evaluated on held-out ImageNet images. The derivations that are present (Propositions 1, 3, 4) manipulate the paper's own definitions without importing a load-bearing self-citation or renaming a known result as a new one. The main caveat is statistical rather than circular: Observation II's zero-mean test (Eq. 12) is an identity under the conditional distribution p(X|y), whereas Table 2 reports means over X_T drawn from the unconditional noise prior, so the large mean for zeta=4.8 may partly reflect E[grad log p(y|X_T)] rather than establishing an invalid score; this weakens one pillar of the MAP case but does not make the argument circular. Because the paper is self-contained against external benchmarks and its core claim is an empirically supported hypothesis with an independent implementation, no circular step meets the evidentiary bar.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The MAP reinterpretation rests on standard Gaussian concentration, two stated approximation assumptions, and a reference-score assumption; the algorithmic results depend on tuned hyperparameters. No new entities are introduced.

free parameters (3)
  • Guidance step size zeta_t = 4.8 for DPS SR, 0.6 for DPS deblur, 9.6 for DMAP(same) SR, 1.2 for DMAP(same) deblur
    Tuned per method and task (Table 8); all quantitative comparisons depend on these choices.
  • Number of gradient ascent steps K = 2 for DMAP(same), 3 for DMAP(full)
    Chosen to trade complexity against performance in Table 5; results vary with K.
  • CSE training set size = 100, 1000, or self-generated images
    Selected to show few-shot capability; Table 6 shows performance grows with dataset size.
assumptions (4)
  • standard math As d grows, the isotropic Gaussian p(X_{t-1}|X_t) concentrates on a sphere of radius sqrt(d)*sigma_t and its log-likelihood converges in probability to a constant (Cover, Theorem 3.1.1).
    Used in Proposition 3 to replace sampling from the transition with optimization on the sphere surface.
  • domain assumption The posterior mean E[X0|Xt] is a perfect approximation to posterior samples from p(X0|Xt) (Assumption 5.1).
    Invoked in Appendix A.3 to show the DPS likelihood term equals exp(-zeta_t ||f(E[X0|Xt])-y||), connecting DPS updates to gradient ascent.
  • domain assumption log p(y|X_{t-1}) is locally linear within radius sqrt(n)*sigma_t and gradients w.r.t. X_{t-1} and X_t are approximately equal (Assumption 5.2).
    Used in the proof of Proposition 6 that DSG, a variant of DPS with projection, solves the MAP problem.
  • domain assumption StableSR provides a reliable estimate of the true conditional score p(X_t|y).
    Observation I computes the error of DPS's score relative to StableSR; if StableSR is far from the true conditional score, the comparison does not establish DPS's error.

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Cite this review

Pith. "Pith review of Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior." pith.science (2026). https://pith.science/paper/G2URZO24

@misc{pith2026250118913,
  author       = {Pith},
  title        = {Pith review of: Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G2URZO24}},
  note         = {Machine review of arXiv:2501.18913}
}
read the original abstract

Recent advancements in diffusion models have been leveraged to address inverse problems without additional training, and Diffusion Posterior Sampling (DPS) (Chung et al., 2022a) is among the most popular approaches. Previous analyses suggest that DPS accomplishes posterior sampling by approximating the conditional score. While in this paper, we demonstrate that the conditional score approximation employed by DPS is not as effective as previously assumed, but rather aligns more closely with the principle of maximizing a posterior (MAP). This assertion is substantiated through an examination of DPS on 512x512 ImageNet images, revealing that: 1) DPS's conditional score estimation significantly diverges from the score of a well-trained conditional diffusion model and is even inferior to the unconditional score; 2) The mean of DPS's conditional score estimation deviates significantly from zero, rendering it an invalid score estimation; 3) DPS generates high-quality samples with significantly lower diversity. In light of the above findings, we posit that DPS more closely resembles MAP than a conditional score estimator, and accordingly propose the following enhancements to DPS: 1) we explicitly maximize the posterior through multi-step gradient ascent and projection; 2) we utilize a light-weighted conditional score estimator trained with only 100 images and 8 GPU hours. Extensive experimental results indicate that these proposed improvements significantly enhance DPS's performance. The source code for these improvements is provided in https://github.com/tongdaxu/Rethinking-Diffusion-Posterior-Sampling-From-Conditional-Score-Estimator-to-Maximizing-a-Posterior.

Figures

Figures reproduced from arXiv: 2501.18913 by the authors.

Figure 2
Figure 2. Qualitative results of different ap￾proaches for SR×8. DPS only works with ζt = 4.8 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The per-pixel standard deviation of DPS is much lower than that of StableSR [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. The image samples from DPS has much lower visual diversity than that of StableSR. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (8 more)
Figure 5
Figure 5. Figure 5: Conceptual illustration of the update procedure of DPS, DSG and DMAP. The green [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Qualitative results on 512 × 512 ImageNet images. Our proposed approaches improve DPS significantly. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Effect of CSE and number of training images. CSE does not work well without DPS. [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: A toy example with 2D 2-GMM and inpainting operator. The true posterior is a 2 modal [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: Visual comparison of DPS reconstruction with Stable Diffusion 1.5 and 2.0. [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: Additional qualitative results for SR×8. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]
Figure 11
Figure 11. Figure 11: Additional qualitative results for Gaussian deblurring. [PITH_FULL_IMAGE:figures/full_fig_p024_11.png]
Figure 12
Figure 12. Figure 12: Additional qualitative results for non-linear deblurring. [PITH_FULL_IMAGE:figures/full_fig_p025_12.png]

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Forward citations

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Reference graph

Works this paper leans on

54 extracted references · 18 canonical work pages · cited by 2 Pith papers

  1. [1]

    Universal guidance for diffusion models

    Arpit Bansal, Hong-Min Chu, Avi Schwarzschild, Soumyadip Sengupta, Micah Goldblum, Jonas Geiping, and Tom Goldstein. Universal guidance for diffusion models. 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pp.\ 843--852, 2023. URL https://api.semanticscholar.org/CorpusID:256846836

    work page 2023

  2. [2]

    Sutherland, Michal Arbel, and Arthur Gretton

    Mikolaj Binkowski, Danica J. Sutherland, Michal Arbel, and Arthur Gretton. Demystifying mmd gans. ArXiv, abs/1801.01401, 2018. URL https://api.semanticscholar.org/CorpusID:3531856

    arXiv 2018

  3. [3]

    Tweedie moment projected diffusions for inverse problems

    Benjamin Boys, Mark Girolami, Jakiw Pidstrigach, Sebastian Reich, Alan Mosca, and O Deniz Akyildiz. Tweedie moment projected diffusions for inverse problems. arXiv preprint arXiv:2310.06721, 2023

    arXiv 2023

  4. [4]

    Monte carlo guided denoising diffusion models for bayesian linear inverse problems

    Gabriel Cardoso, Yazid Janati el idrissi, Sylvain Le Corff, and Eric Moulines. Monte carlo guided denoising diffusion models for bayesian linear inverse problems. In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=nHESwXvxWK

    2024

  5. [5]

    McCann, Marc Louis Klasky, and J

    Hyungjin Chung, Jeongsol Kim, Michael T. McCann, Marc Louis Klasky, and J. C. Ye. Diffusion posterior sampling for general noisy inverse problems. ArXiv, abs/2209.14687, 2022 a . URL https://api.semanticscholar.org/CorpusID:252596252

    arXiv 2022

  6. [6]

    Hyungjin Chung, Byeongsu Sim, Dohoon Ryu, and J. C. Ye. Improving diffusion models for inverse problems using manifold constraints. ArXiv, abs/2206.00941, 2022 b . URL https://api.semanticscholar.org/CorpusID:249282628

    arXiv 2022

  7. [7]

    Prompt-tuning latent diffusion models for inverse problems

    Hyungjin Chung, Jong Chul Ye, Peyman Milanfar, and Mauricio Delbracio. Prompt-tuning latent diffusion models for inverse problems. ArXiv, abs/2310.01110, 2023. URL https://api.semanticscholar.org/CorpusID:263605744

    arXiv 2023

  8. [8]

    From posterior sampling to meaningful diversity in image restoration

    Noa Cohen, Hila Manor, Yuval Bahat, and Tomer Michaeli. From posterior sampling to meaningful diversity in image restoration. ArXiv, abs/2310.16047, 2023. URL https://api.semanticscholar.org/CorpusID:264439486

    arXiv 2023

Show all 54 references
  1. [9]

    Elements of information theory

    Thomas M Cover. Elements of information theory. John Wiley & Sons, 1999

    1999

  2. [10]

    Closing the ode-sde gap in score-based diffusion models through the fokker-planck equation

    Teo Deveney, Jan Stanczuk, Lisa Maria Kreusser, Chris Budd, and Carola-Bibiane Sch \"o nlieb. Closing the ode-sde gap in score-based diffusion models through the fokker-planck equation. arXiv preprint arXiv:2311.15996, 2023

    2023 arXiv

  3. [11]

    Diffusion models beat gans on image synthesis

    Prafulla Dhariwal and Alex Nichol. Diffusion models beat gans on image synthesis. ArXiv, abs/2105.05233, 2021. URL https://api.semanticscholar.org/CorpusID:234357997

    2021 arXiv

  4. [12]

    Diffusion posterior sampling for linear inverse problem solving: A filtering perspective

    Zehao Dou and Yang Song. Diffusion posterior sampling for linear inverse problem solving: A filtering perspective. In The Twelfth International Conference on Learning Representations, 2023

    2023

  5. [13]

    Diffusion posterior sampling for linear inverse problem solving: A filtering perspective

    Zehao Dou and Yang Song. Diffusion posterior sampling for linear inverse problem solving: A filtering perspective. In The Twelfth International Conference on Learning Representations, 2024

    2024

  6. [14]

    Score-based diffusion models as principled priors for inverse imaging

    Berthy T Feng, Jamie Smith, Michael Rubinstein, Huiwen Chang, Katherine L Bouman, and William T Freeman. Score-based diffusion models as principled priors for inverse imaging. arXiv preprint arXiv:2304.11751, 2023

    2023 arXiv

  7. [15]

    Inverse problems with diffusion models: A map estimation perspective

    Sai Bharath Chandra Gutha, Ricardo Vinuesa, and Hossein Azizpour. Inverse problems with diffusion models: A map estimation perspective. arXiv preprint arXiv:2407.20784, 2024

    2024 arXiv

  8. [16]

    Fast and stable diffusion inverse solver with history gradient update

    Linchao He, Hongyu Yan, Mengting Luo, Kunming Luo, Wang Wang, Wenchao Du, Hu Chen, Hong ling Yang, and Yan Zhang. Fast and stable diffusion inverse solver with history gradient update. 2023. URL https://api.semanticscholar.org/CorpusID:260124974

    2023

  9. [17]

    Manifold preserving guided diffusion

    Yutong He, Naoki Murata, Chieh-Hsin Lai, Yuhta Takida, Toshimitsu Uesaka, Dongjun Kim, Wei-Hsiang Liao, Yuki Mitsufuji, J Zico Kolter, Ruslan Salakhutdinov, et al. Manifold preserving guided diffusion. In The Twelfth International Conference on Learning Representations, 2024. ...

    2024

  10. [18]

    Gans trained by a two time-scale update rule converge to a local nash equilibrium

    Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. In Neural Information Processing Systems, 2017. URL https://api.semanticscholar.org/CorpusID:326772

    2017

  11. [19]

    Denoising diffusion probabilistic models

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33: 0 6840--6851, 2020

    2020

  12. [20]

    Divide-and-conquer posterior sampling for denoising diffusion priors

    Yazid Janati, Alain Durmus, Eric Moulines, and Jimmy Olsson. Divide-and-conquer posterior sampling for denoising diffusion priors. arXiv preprint arXiv:2403.11407, 2024

    2024 arXiv

  13. [21]

    Elucidating the design space of diffusion-based generative models

    Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine. Elucidating the design space of diffusion-based generative models. ArXiv, abs/2206.00364, 2022. URL https://api.semanticscholar.org/CorpusID:249240415

    2022 arXiv

  14. [22]

    Denoising diffusion restoration models

    Bahjat Kawar, Michael Elad, Stefano Ermon, and Jiaming Song. Denoising diffusion restoration models. ArXiv, abs/2201.11793, 2022. URL https://api.semanticscholar.org/CorpusID:246411364

    2022 arXiv

  15. [23]

    Kingma and Jimmy Ba

    Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. CoRR, abs/1412.6980, 2014. URL https://api.semanticscholar.org/CorpusID:6628106

    2014 arXiv

  16. [24]

    Indoor scene layout estimation from a single image

    Hung-Jin Lin, Sheng-Wei Huang, Shang-Hong Lai, and Chen-Kuo Chiang. Indoor scene layout estimation from a single image. 2018 24th International Conference on Pattern Recognition (ICPR), pp.\ 842--847, 2018. URL https://api.semanticscholar.org/CorpusID:54212984

    2018

  17. [25]

    Flow matching for generative modeling

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

    2022 arXiv

  18. [26]

    Repaint: Inpainting using denoising diffusion probabilistic models

    Andreas Lugmayr, Martin Danelljan, Andr \'e s Romero, Fisher Yu, Radu Timofte, and Luc Van Gool. Repaint: Inpainting using denoising diffusion probabilistic models. 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp.\ 11451--11461, 2022. URL https:/...

    2022

  19. [28]

    A variational perspective on solving inverse problems with diffusion models

    Morteza Mardani, Jiaming Song, Jan Kautz, and Arash Vahdat. A variational perspective on solving inverse problems with diffusion models. arXiv preprint arXiv:2305.04391, 2023 b

    2023 arXiv

  20. [29]

    Pulse: Self-supervised photo upsampling via latent space exploration of generative models

    Sachit Menon, Alexandru Damian, Shijia Hu, Nikhil Ravi, and Cynthia Rudin. Pulse: Self-supervised photo upsampling via latent space exploration of generative models. 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp.\ 2434--2442, 2020. URL https://...

    2020

  21. [30]

    Variational inference for monte carlo objectives

    Andriy Mnih and Danilo Rezende. Variational inference for monte carlo objectives. In International Conference on Machine Learning, pp.\ 2188--2196. PMLR, 2016

    2016

  22. [31]

    Monte carlo gradient estimation in machine learning

    Shakir Mohamed, Mihaela Rosca, Michael Figurnov, and Andriy Mnih. Monte carlo gradient estimation in machine learning. Journal of Machine Learning Research, 21 0 (132): 0 1--62, 2020

    2020

  23. [32]

    Particle denoising diffusion sampler

    Angus Phillips, Hai-Dang Dau, Michael John Hutchinson, Valentin De Bortoli, George Deligiannidis, and Arnaud Doucet. Particle denoising diffusion sampler. ArXiv, abs/2402.06320, 2024. URL https://api.semanticscholar.org/CorpusID:267616914

    2024 arXiv

  24. [33]

    Training-free linear image inversion via flows

    Ashwini Pokle, Matthew J Muckley, Ricky TQ Chen, and Brian Karrer. Training-free linear image inversion via flows. arXiv preprint arXiv:2310.04432, 2023

    2023 arXiv

  25. [34]

    Muckley, Ricky T

    Ashwini Pokle, Matthew J. Muckley, Ricky T. Q. Chen, and Brian Karrer. Training-free linear image inversion via flows, 2024. URL https://openreview.net/forum?id=3JoQqW35GQ

    2024

  26. [35]

    Beyond first-order tweedie: Solving inverse problems using latent diffusion

    Litu Rout, Yujia Chen, Abhishek Kumar, Constantine Caramanis, Sanjay Shakkottai, and Wen-Sheng Chu. Beyond first-order tweedie: Solving inverse problems using latent diffusion. ArXiv, abs/2312.00852, 2023. URL https://api.semanticscholar.org/CorpusID:265609906

    2023 arXiv

  27. [36]

    Solving linear inverse problems provably via posterior sampling with latent diffusion models

    Litu Rout, Negin Raoof, Giannis Daras, Constantine Caramanis, Alex Dimakis, and Sanjay Shakkottai. Solving linear inverse problems provably via posterior sampling with latent diffusion models. Advances in Neural Information Processing Systems, 36, 2024

    2024

  28. [37]

    Deep unsupervised learning using nonequilibrium thermodynamics

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

    2015

  29. [38]

    Solving inverse problems with latent diffusion models via hard data consistency

    Bowen Song, Soo Min Kwon, Zecheng Zhang, Xinyu Hu, Qing Qu, and Liyue Shen. Solving inverse problems with latent diffusion models via hard data consistency. arXiv preprint arXiv:2307.08123, 2023 a

    2023 arXiv

  30. [39]

    Pseudoinverse-guided diffusion models for inverse problems

    Jiaming Song, Arash Vahdat, Morteza Mardani, and Jan Kautz. Pseudoinverse-guided diffusion models for inverse problems. In International Conference on Learning Representations, 2022

    2022

  31. [40]

    Pseudoinverse-guided diffusion models for inverse problems

    Jiaming Song, Arash Vahdat, Morteza Mardani, and Jan Kautz. Pseudoinverse-guided diffusion models for inverse problems. In International Conference on Learning Representations, 2023 b

    2023

  32. [41]

    Loss-guided diffusion models for plug-and-play controllable generation

    Jiaming Song, Qinsheng Zhang, Hongxu Yin, Morteza Mardani, Ming-Yu Liu, Jan Kautz, Yongxin Chen, and Arash Vahdat. Loss-guided diffusion models for plug-and-play controllable generation. In International Conference on Machine Learning, 2023 c . URL https://api.semanticscholar....

    2023

  33. [42]

    Score-based generative modeling through stochastic differential equations

    Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456, 2020

    2011 arXiv

  34. [43]

    Exploiting diffusion prior for real-world image super-resolution

    Jianyi Wang, Zongsheng Yue, Shangchen Zhou, Kelvin CK Chan, and Chen Change Loy. Exploiting diffusion prior for real-world image super-resolution. International Journal of Computer Vision, pp.\ 1--21, 2024

    2024

  35. [44]

    Zero-shot image restoration using denoising diffusion null-space model

    Yinhuai Wang, Jiwen Yu, and Jian Zhang. Zero-shot image restoration using denoising diffusion null-space model. ArXiv, abs/2212.00490, 2022. URL https://api.semanticscholar.org/CorpusID:254125609

    2022 arXiv

  36. [45]

    Simple statistical gradient-following algorithms for connectionist reinforcement learning

    Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine learning, 8: 0 229--256, 1992

    1992

  37. [46]

    Practical and asymptotically exact conditional sampling in diffusion models

    Luhuan Wu, Brian Trippe, Christian Naesseth, David Blei, and John P Cunningham. Practical and asymptotically exact conditional sampling in diffusion models. Advances in Neural Information Processing Systems, 36, 2024

    2024

  38. [47]

    Guidance with spherical gaussian constraint for conditional diffusion

    Lingxiao Yang, Shutong Ding, Yifan Cai, Jingyi Yu, Jingya Wang, and Ye Shi. Guidance with spherical gaussian constraint for conditional diffusion. arXiv preprint arXiv:2402.03201, 2024

    2024 arXiv

  39. [48]

    Freedom: Training-free energy-guided conditional diffusion model

    Jiwen Yu, Yinhuai Wang, Chen Zhao, Bernard Ghanem, and Jian Zhang. Freedom: Training-free energy-guided conditional diffusion model. ArXiv, abs/2303.09833, 2023. URL https://api.semanticscholar.org/CorpusID:257622962

    2023 arXiv

  40. [49]

    Improving diffusion inverse problem solving with decoupled noise annealing

    Bingliang Zhang, Wenda Chu, Julius Berner, Chenlin Meng, Anima Anandkumar, and Yang Song. Improving diffusion inverse problem solving with decoupled noise annealing. arXiv preprint arXiv:2407.01521, 2024

    2024 arXiv

  41. [50]

    Adding conditional control to text-to-image diffusion models

    Lvmin Zhang, Anyi Rao, and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. ArXiv, abs/2302.05543, 2023. URL https://api.semanticscholar.org/CorpusID:256827727

    2023 arXiv

  42. [51]

    Efros, Eli Shechtman, and Oliver Wang

    Richard Zhang, Phillip Isola, Alexei A. Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.\ 586--595, 2018. URL https://api.semanticscholar.org/...

    2018

  43. [52]

    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 gl...

  44. [53]

    @esa (Ref

    \@ifxundefined[1] #1\@undefined \@firstoftwo \@secondoftwo \@ifnum[1] #1 \@firstoftwo \@secondoftwo \@ifx[1] #1 \@firstoftwo \@secondoftwo [2] @ #1 \@temptokena #2 #1 @ \@temptokena \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should ...

  45. [54]

    \@lbibitem[] @bibitem@first@sw\@secondoftwo \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 @tmp #1 NAT@b@open@#2 NAT@b@shut@#2 \@ifnum @merge>\@ne @bibitem@firs...

  46. [55]

    @open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifxundefined @sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifxundefined @heading @heading NAT@ctr thebibliography [1] @ \@biblabel @NAT@ctr \@bibset...

Pith tools

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