Pith. sign in

REVIEW 2 major objections 4 minor 41 references

SlerpFlow claims that replacing Euclidean velocity averaging with a spherical chord removes the radial drift that degrades rectified-flow inversion, yielding second-order accuracy at first-order cost.

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

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

T0 review · deepseek-v4-flash

2026-08-01 07:49 UTC pith:G5BXXJNP

load-bearing objection SlerpFlow is a genuinely new geometric heuristic for FLUX inversion, but its central second-order accuracy claim is false because the α=0.5 slerp halves the tangential velocity. the 2 major comments →

arxiv 2607.21326 v1 pith:G5BXXJNP submitted 2026-07-23 cs.CV

SlerpFlow: Spherical Trajectory Correction for Rectified Flow Inversion

Wenbin Duan , Yan Shu , Zhuoyuan Fu , Fangmin Zhao , Yan Li , Yaru Zhao , Binyang Li This is my paper
classification cs.CV
keywords rectified flow inversionspherical linear interpolation (slerp)FLUXmanifold hypothesiscentrifugal driftimage editingzero-shotdiscretization error
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that the dominant source of error when inverting a rectified-flow model like FLUX is not ordinary discretization error but a 'spurious centrifugal drift': any Euclidean solver step with a tangential velocity slightly inflates the latent norm, pushing the trajectory off the thin spherical shell where real latents concentrate. The proposed fix, SlerpFlow, decouples each step into a radial update and an angular update, replacing the Euclidean velocity average with spherical linear interpolation (slerp) between the current and predicted directions, then reconstructs a chordal velocity that lands exactly on the predicted radius. Because the corrected velocity is cached, the method claims second-order accuracy at the cost of one new model evaluation per step. If correct, this means higher-fidelity image reconstruction and stronger prompt alignment in zero-shot editing of existing FLUX models, with no retraining.

Core claim

On its own terms, SlerpFlow's discovery is that the recurring failure of rectified-flow inversion is not primarily high-order truncation error but a systematic geometric error it calls spurious centrifugal drift: when a Euclidean solver takes a step whose velocity has any component tangent to the latent shell, the step's squared norm gains h² times the tangential speed squared, so the trajectory spirals outward from the thin spherical shell where high-dimensional latents concentrate. SlerpFlow therefore decouples each integration step in polar coordinates. It predicts the next radius linearly, ρ_next = ρ_t + h⟨Z_t/ρ_t, v̄⟩, and sets the next direction not by Euclidean normalization but by sp

What carries the argument

The central object is the slerp operator u ∗_α v = [sin((1−α)Ω)/sin Ω]u + [sin(αΩ)/sin Ω]v, with Ω = arccos⟨u,v⟩ — spherical linear interpolation along the geodesic on the unit sphere — embedded in a Decoupled Chordal Update Z_{t+h} = ρ_next d_next. The slerp replaces the Euclidean tangent step for the angular part, so the quadratic norm inflation h²‖v⊥‖² never appears, while the radial part is updated by a one-step linear estimate; the cached velocity makes the whole correction free of extra model evaluations.

Load-bearing premise

The load-bearing premise is that each local step of the latent trajectory behaves like pure rotation on a sphere of constant radius—so the slerp chord at α=0.5 coincides with the trapezoidal average of the endpoint velocities and the radial update is exact; on real FLUX trajectories, where the norm changes, this equivalence is only approximate.

What would settle it

Take a real image, invert it with FLUX using a fine RK4 integrator as the reference trajectory, then: (1) measure ⟨Z_t, v_t⟩/‖Z_t‖ along the path—if it is not near zero, the pure-rotation premise fails; (2) compare slerp(d_t, d_euler, 0.5) with the normalized mean (d_t + d̂_{t+h})/2—if they differ by more than O(h²), the second-order claim lacks its stated geometric justification; (3) record ‖Z_{t+h}‖ − ρ_next for SlerpFlow steps—if the norm drifts, the 'exact on the predicted shell' property is violated.

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

If this is right

  • At a matched budget of 15 steps, SlerpFlow reports higher PSNR/SSIM and lower LPIPS than Euler, Heun, RF-Solver, and FireFlow for both conditional and unconditional FLUX reconstruction on PIE-Bench.
  • For text-guided editing, SlerpFlow attains the highest CLIP whole-image and edited-region similarity scores, at the cost of marginally weaker background preservation on some metrics.
  • The paper's convergence curve indicates SlerpFlow acts as a geometric regularizer for moderate step budgets rather than an extreme few-step accelerator; below very low step counts it does not dominate.
  • The same slerp correction transfers to SD3, giving modest reconstruction gains over FireFlow and supporting the generality of the spherical prior.
  • No training or per-model adaptation is needed, so the correction can be dropped into existing inversion/editing pipelines for rectified-flow transformers.

Where Pith is reading between the lines

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

  • If the spurious centrifugal drift is the dominant error, SlerpFlow's improvement should grow with tangential velocity magnitude and with step count; measuring reconstruction error as a function of ‖v⊥‖ would test the causal story directly.
  • The same decoupling could be applied to the forward generation pass, not just inversion—correcting radial drift during sampling might improve few-step generation quality in FLUX-like models.
  • Figure 5's non-uniform angular correction suggests a per-step schedule of α, or an adaptive estimate from local curvature, could outperform the fixed α=0.5; that is a testable extension the paper leaves implicit.
  • Because the theoretical derivation assumes pure rotation, the method's success on real FLUX likely depends on α being an empirical fit; flows with stronger radial dynamics would be the test case.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. SlerpFlow is a training-free solver for rectified-flow inversion/editing. It proposes to decouple the latent update into radial and angular components, predict a target radius, use spherical linear interpolation (Slerp) with α=0.5 between the current direction and an Euler-predicted direction, and then form a chordal velocity update. The paper claims that this update is second-order accurate, with local truncation error O(h^3) and global order O(h^2), and reports improved FLUX reconstruction and editing metrics on PIE-Bench compared with Euler, Heun, RF-Solver, and FireFlow. The central theoretical claim is that SlerpFlow's effective velocity equals the trapezoidal mean of the endpoint velocities, so that the scheme matches the exact trajectory up to O(h^2).

Significance. If the central theoretical claim were correct, SlerpFlow would be an elegant and valuable contribution: a zero-training, constant-NFE solver that attains second-order accuracy while respecting a geometric manifold prior. The paper also ships code, reports careful NFE accounting, and includes an extra SD3 ablation. However, the paper's central mathematical claim is demonstrably false for the algorithm actually implemented. The update computed by Algorithm 1 is not the trapezoidal mean; its tangential component is halved, so the scheme is not even consistent with the original rectified-flow ODE as h→0. Consequently the claimed theoretical validation does not hold, and the strong empirical numbers would need to be reinterpreted as the outcome of an unexplained empirical regularizer rather than a second-order geometric solver. This substantially reduces the paper's significance in its present form.

major comments (2)
  1. [Appendix B.2 / C.2, Eqs. (13), (20); Algorithm 1] The central equivalence v_slerp ≈ (v(t)+v(t+h))/2 is false for the implemented update. Let Z_t = ρ u and decompose the averaged velocity as v̄ = v_r u + v_p with v_p ⟂ u. Algorithm 1 sets d_euler = normalize(Z_t + h v̄) ≈ u + h v_p/ρ, and Slerp(d_t, d_euler, 0.5) ≈ u + h v_p/(2ρ). With ρ_next = ρ + h v_r, the chordal update gives v_slerp ≈ v_r u + ½ v_p + O(h). Thus the tangential velocity is halved. In the pure-rotation case considered in Eq. (15), v_slerp ≈ ½ v_t, so the scheme is inconsistent with dZ/dt = v_t; the global error does not vanish as h→0, and the claimed LTE O(h^3)/global O(h^2) is incorrect. Equation (20) would hold only for α=1, i.e. taking the Euler endpoint direction, not Algorithm 1's α=0.5. This invalidates the paper's central theoretical justification.
  2. [Section 3.2 / Definition 4.1 / Appendix C.1] The theoretical framework does not justify the crucial choice α=0.5. The analysis of 'centripetal force' and 'spurious centrifugal drift' is derived under the pure-rotation assumption ⟨Z_t, v_t⟩ = 0 (Eq. 15), which the paper itself acknowledges is violated by real flows. No independent estimate of the shell radius or local curvature is provided, and Figure 5 shows that the actual interpolation angle varies along the trajectory, which is consistent with data-dependent geometry but not with a fixed correction. The claimed second-order property is used to motivate the method and the choice α=0.5, but that property does not follow. Since α is described as the only SlerpFlow-specific hyperparameter and no sensitivity analysis is reported, the method's performance currently rests on an unexplained empirical fit rather than the stated theory.
minor comments (4)
  1. [Abstract / Introduction] There are numerous typographical and grammatical errors, e.g. 'without additional training.Code is available', 'tore-spect', 'isgrounded', and inconsistent capitalization. The paper would benefit from a careful editing pass.
  2. [Eq. (8)] The radial decomposition notation is unclear: ∥v_∥∥ and ∥v_⊥∥ are defined, but ⟨Z_t, v_∥⟩ should be replaced by a projection onto the unit radial direction to be rigorous. Specify that v_∥ = ⟨Z_t/ρ_t, v_t⟩ Z_t/ρ_t.
  3. [Algorithm 1 / Section 4.2] Algorithm 1 hard-codes α=0.5 in the Slerp call, while the text calls α a hyperparameter. If α is tunable, report its value and sensitivity; if fixed, say so explicitly.
  4. [Section 5.2 / Figure 4] The caption of Figure 4 says SlerpFlow 'reaches competitive reconstruction accuracy', but the abstract claims it 'improves reconstruction fidelity'. The paper should reconcile these statements and report confidence intervals or significance tests, since the reported gains over FireFlow are small in some metrics.

Circularity Check

1 steps flagged

The O(h^2) convergence proof assumes the trapezoidal-mean property it needs to prove; Algorithm 1's actual slerp chord gives a halved tangential velocity.

specific steps
  1. self definitional [Appendix C.2 / Eq. (20); Appendix B.2 / Eq. (13); Algorithm 1 lines 12-16]
    "In the limit of small step size h, the geodesic chord constructed by Slerp asymptotically aligns with the arithmetic mean of the tangent vectors at the endpoints (trapezoidal integration): vslerp ≈ v(t)+v(t+h)/2. (20) ... d_next ← Slerp(d_t, d_euler, 0.5){Corrected Direction} ... v_slerp ← (ρ_next d_next − Z_t)/h ... Z_{t+1} ← Z_t + h·v_slerp."

    The proof derives LTE O(h^3) and global O(h^2) by substituting Eq. (20) into the linear update, but Eq. (20) is not derived from Algorithm 1. From Algorithm 1's own construction, with u=Z_t/ρ_t and ar v=v_t+O(h), one has d_euler ≈ u + h v_perp/ρ_t, and the α=0.5 Slerp gives d_next ≈ u + h v_perp/(2ρ_t); hence v_slerp = (ρ_next d_next − Z_t)/h ≈ v_rad u + ½ v_perp, not ar v. Under the paper's own pure-rotation assumption ⟨Z_t,v_t⟩=0, this is ½v_t, so the update is inconsistent with the original ODE. The claimed second-order match is exactly the trapezoidal-rule statement inserted as Eq. (20); the conclusion is contained in the premise rather than following from the algorithm.

full rationale

The only load-bearing circular step is in the convergence proof: Appendix B.2/C.2 posits the trapezoidal identification (Eq. 20) and then reads off second-order accuracy from it, while Algorithm 1's defining equations give a different small-h velocity (half the tangential component under pure rotation). This makes the theoretical O(h^2) claim a conclusion assumed in the premise rather than a consequence of the construction. I do not find other circularity: the spherical-shell assumption is stated explicitly (Sec. 3.2, App. C.1, App. E.1) and is not smuggled via self-citation; the α=0.5 weight is a fixed hyperparameter rather than a fitted parameter re-reported as a prediction; Fig. 5's angle profile is descriptive; and the self-citations to Shu et al./Zeng et al. are related-work references, not load-bearing. The reconstruction/editing results are benchmarked against external baselines on PIE-Bench and SD3, so the empirical claims stand or fall independently of the flawed proof. Score 6 reflects the partial circularity of the central theoretical derivation, not the empirical contribution.

Axiom & Free-Parameter Ledger

1 free parameters · 4 axioms · 1 invented entities

The method rests on the spherical-shell hypothesis and the pure-rotation idealization; the proof of second-order accuracy relies on an unproved and false equivalence between the slerp midpoint and the trapezoidal mean. The only fitted parameter is α, which directly controls the correction strength and is not predicted by the theory.

free parameters (1)
  • interpolation weight α = 0.5 (default; not swept in main text)
    Controls the strength of spherical correction. The claimed second-order accuracy in Appendix B.2 requires the endpoint direction (α=1), but the algorithm uses the midpoint (α=0.5); the value is a hyperparameter tuned for the reported results, not derived from the geometry.
axioms (4)
  • domain assumption Latent states concentrate near a thin hyperspherical shell (Manifold Hypothesis)
    Invoked in Section 3.2 and Appendix E.1 to justify spherical interpolation. The paper admits this may fail for anisotropic or locally flat manifolds.
  • domain assumption Locally spherical dynamics: the velocity field can be treated as pure rotation (⟨Zt, vt⟩=0)
    Used in Appendix C.1, Eq. (15), to derive the 'spurious centrifugal drift' O(h²) radial error. Real FLUX trajectories have significant radial dynamics, so the derivation is an idealization, not a description of the actual flow.
  • ad hoc to paper The slerp midpoint chord equals the trapezoidal mean of endpoint velocities
    Asserted in Appendix B.2, Eq. (20) without proof. A small-angle expansion shows the α=0.5 midpoint advances the tangential direction half as fast as the trapezoidal mean; the equivalence would require α=1, contradicting the implemented algorithm.
  • standard math The learned velocity field is sufficiently smooth for a second-order Taylor expansion
    Standard smoothness assumption for LTE/global-error analysis; not the load-bearing issue.
invented entities (1)
  • centripetal force (geometric interpretation of trajectory curvature) no independent evidence
    purpose: Motivates why the flow curves and why the update should follow the sphere rather than a straight line.
    The h²||v⊥||² term is a real algebraic consequence of the norm expansion, but its interpretation as a necessary manifold-preserving force is asserted without independent measurement or falsifiable consequence; no experiment distinguishes the 'force' interpretation from ordinary discretization error.

pith-pipeline@v1.3.0-alltime-deepseek · 15290 in / 28457 out tokens · 278962 ms · 2026-08-01T07:49:15.582814+00:00 · methodology

0 comments
read the original abstract

Rectified-flow-based diffusion transformers, particularly FLUX, have demonstrated outstanding performance in high-quality image generation. However, achieving fast and accurate inversion--transforming images back to latent noise for faithful reconstruction and editing--remains a challenging bottleneck due to the discretization errors of linear solvers. This paper introduces SlerpFlow, a straightforward yet highly effective zero-shot approach that unlocks the full potential of FLUX for high-fidelity inversion and editing. Unlike existing approaches (e.g., RF-Solver) that rely on complex numerical approximations such as high-order Taylor expansions to correct trajectory errors, we present a geometric view based on the Manifold Hypothesis: the empirically observed trajectory curvature is not a numerical artifact, but rather serves as a necessary "centripetal force" that constrains the flow to remain on the data manifold. Guided by this insight, SlerpFlow integrates Spherical Linear Interpolation (Slerp) to rectify flow velocity directions on the hypersphere, strictly adhering to the intrinsic curvature of the latent space. Crucially, by caching the corrected velocity for subsequent steps, SlerpFlow achieves high-precision inversion while maintaining the computational efficiency of a first-order Euler solver. Extensive experiments on FLUX-based reconstruction and editing tasks demonstrate that SlerpFlow improves reconstruction fidelity and achieves stronger semantic alignment in editing without requiring additional training. Code is available at https://github.com/0answer0/SlerpFlow.

Figures

Figures reproduced from arXiv: 2607.21326 by Binyang Li, Fangmin Zhao, Wenbin Duan, Yan Li, Yan Shu, Yaru Zhao, Zhuoyuan Fu.

Figure 1
Figure 1. Figure 1: Geometric interpretation of discretization errors. We illustrate why standard solvers fail on curved manifolds (a) and how our proposed Decoupled Chordal Update (b) eliminates the radial drift by strictly adhering to the intrinsic geometry. than being a numerical artifact, this curvature emerges as a geometric necessity. Given that natural data resides on a low￾dimensional manifold M ⊂ R D—and that velocit… view at source ↗
Figure 2
Figure 2. Figure 2: Qualitative results of image reconstruction. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Qualitative comparison on image editing. Evaluation Metrics. All quantitative experiments are con￾ducted on the PIE-Bench dataset (Ju et al., 2024). We em￾ploy a comprehensive set of metrics to evaluate performance across three distinct dimensions: • Reconstruction Quality & Background Preserva￾tion: To assess the fidelity of inversion and the preser￾vation of unedited regions, we utilize four standard met… view at source ↗
Figure 4
Figure 4. Figure 4: Convergence comparison. Reconstruction RMSE of RF-Solver, FireFlow, and SlerpFlow under different sampling steps. SlerpFlow shows decreasing error as the sampling budget increases and reaches competitive reconstruction accuracy in the middle-to-high step range [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

discussion (0)

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

Reference graph

Works this paper leans on

41 extracted references · 2 linked inside Pith

  1. [1]

    Chen, Ricky T. Q. and Rubanova, Yulia and Bettencourt, Jesse and Duvenaud, David , title =. Advances in Neural Information Processing Systems , volume =

  2. [2]

    The Eleventh International Conference on Learning Representations , year =

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

  3. [3]

    The Eleventh International Conference on Learning Representations , year =

    Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow , author =. The Eleventh International Conference on Learning Representations , year =

  4. [4]

    and Kumar, Abhishek and Ermon, Stefano and Poole, Ben , title =

    Song, Yang and Sohl-Dickstein, Jascha and Kingma, Diederik P. and Kumar, Abhishek and Ermon, Stefano and Poole, Ben , title =. International Conference on Learning Representations , year =

  5. [5]

    International Conference on Learning Representations (ICLR) , year =

    Denoising Diffusion Implicit Models , author =. International Conference on Learning Representations (ICLR) , year =

  6. [6]

    International Conference on Learning Representations (ICLR) , year =

    FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models , author =. International Conference on Learning Representations (ICLR) , year =

  7. [7]

    International Conference on Learning Representations (ICLR) , year =

    Lightning-Fast Image Inversion and Editing for Text-to-Image Diffusion Models , author =. International Conference on Learning Representations (ICLR) , year =

  8. [8]

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

    NULL-Text Inversion for Editing Real Images Using Guided Diffusion Models , author =. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , pages =. 2023 , doi =

    2023

  9. [9]

    Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) , year =

    Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models , author =. Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) , year =. doi:10.1109/ICCV51070.2023.00683 , url =

    arXiv 2023

  10. [10]

    Proceedings of the Winter Conference on Applications of Computer Vision (WACV) , pages =

    Negative-Prompt Inversion: Fast Image Inversion for Editing with Text-guided Diffusion Models , author =. Proceedings of the Winter Conference on Applications of Computer Vision (WACV) , pages =. 2025 , url =

    2025

  11. [11]

    Advances in Neural Information Processing Systems (NeurIPS) , year =

    FreeInv: Free Lunch for Improving DDIM Inversion , author =. Advances in Neural Information Processing Systems (NeurIPS) , year =

  12. [12]

    International Conference on Learning Representations (ICLR) , year =

    PnP Inversion: Boosting Diffusion-based Editing with 3 Lines of Code , author =. International Conference on Learning Representations (ICLR) , year =

  13. [13]

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

    EDICT: Exact Diffusion Inversion via Coupled Transformations , author =. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , year =

  14. [14]

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

    Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion , author =. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , year =

  15. [15]

    International Conference on Learning Representations (ICLR) , year =

    Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations , author =. International Conference on Learning Representations (ICLR) , year =

  16. [16]

    Advances in Neural Information Processing Systems (NeurIPS) , pages =

    Invertible Consistency Distillation for Text-Guided Image Editing in Around 7 Steps , author =. Advances in Neural Information Processing Systems (NeurIPS) , pages =. 2024 , url =

    2024

  17. [17]

    Advances in Neural Information Processing Systems (NeurIPS) , pages =

    Improving the Training of Rectified Flows , author =. Advances in Neural Information Processing Systems (NeurIPS) , pages =. 2024 , doi =

    2024

  18. [18]

    Proceedings of the 42nd International Conference on Machine Learning (ICML) , series =

    Taming Rectified Flow for Inversion and Editing , author =. Proceedings of the 42nd International Conference on Machine Learning (ICML) , series =. 2025 , publisher =

    2025

  19. [19]

    Proceedings of the 42nd International Conference on Machine Learning (ICML) , series =

    FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing , author =. Proceedings of the 42nd International Conference on Machine Learning (ICML) , series =. 2025 , publisher =

    2025

  20. [20]

    The Eleventh International Conference on Learning Representations , year =

    Prompt-to-Prompt Image Editing with Cross-Attention Control , author =. The Eleventh International Conference on Learning Representations , year =

  21. [21]

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

    Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation , author =. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , year =

  22. [22]

    Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) , pages =

    MasaCtrl: Tuning-Free Mutual Self-Attention Control for Consistent Image Synthesis and Editing , author =. Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) , pages =. 2023 , doi =

    2023

  23. [23]

    International Conference on Learning Representations (ICLR) , year =

    Add-it: Training-Free Object Insertion in Images with Pretrained Diffusion Models , author =. International Conference on Learning Representations (ICLR) , year =

  24. [24]

    Engineering , volume =

    A Geometric Understanding of Deep Learning , author =. Engineering , volume =. 2020 , doi =

    2020

  25. [25]

    Journal of the American Mathematical Society , volume =

    Testing the Manifold Hypothesis , author =. Journal of the American Mathematical Society , volume =. 2016 , doi =

    2016

  26. [26]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , volume =

    Representation Learning: A Review and New Perspectives , author =. IEEE Transactions on Pattern Analysis and Machine Intelligence , volume =. 2013 , doi =

    2013

  27. [27]

    Forty-second International Conference on Machine Learning,

    Zhengyu Zhou and Weiwei Liu , title =. Forty-second International Conference on Machine Learning,. 2025 , url =

    2025

  28. [28]

    Proceedings of the 41st International Conference on Machine Learning , series =

    Diffusion Models Encode the Intrinsic Dimension of Data Manifolds , author =. Proceedings of the 41st International Conference on Machine Learning , series =. 2024 , month =

    2024

  29. [29]

    SIAM Journal on Computing , volume =

    A Topological View of Unsupervised Learning from Noisy Data , author =. SIAM Journal on Computing , volume =. 2011 , doi =

    2011

  30. [30]

    Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics , series =

    Minimax Rates for Homology Inference , author =. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics , series =. 2012 , publisher =

    2012

  31. [31]

    2018 , doi =

    Roman Vershynin , title =. 2018 , doi =

    2018

  32. [32]

    and Ghanbari, M

    Huynh-Thu, Q. and Ghanbari, M. , journal =. Scope of validity of. 2008 , doi =

    2008

  33. [33]

    IEEE Transactions on Image Processing , volume =

    Image Quality Assessment: From Error Visibility to Structural Similarity , author =. IEEE Transactions on Image Processing , volume =. 2004 , doi =

    2004

  34. [34]

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

    The Unreasonable Effectiveness of Deep Features as a Perceptual Metric , author =. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , pages =. 2018 , doi =

    2018

  35. [35]

    Proceedings of the 38th International Conference on Machine Learning (ICML) , series =

    Radford, Alec and Kim, Jong Wook and Hallacy, Chris and Ramesh, Aditya and Goh, Gabriel and Agarwal, Sandhini and Sastry, Girish and Askell, Amanda and Mishkin, Pamela and Clark, Jack and Krueger, Gretchen and Sutskever, Ilya , title =. Proceedings of the 38th International Conference on Machine Learning (ICML) , series =. 2021 , publisher =

    2021

  36. [36]

    2024 , month = aug, howpublished =

    Announcing Black Forest Labs (FLUX.1 Model Family) , author =. 2024 , month = aug, howpublished =

    2024

  37. [37]

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

    Inversion-Free Image Editing with Language-Guided Diffusion Models , author =. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , pages =. 2024 , url =

    2024

  38. [38]

    2026 , url =

    Jiao, Guanlong and Huang, Biqing and Wang, Kuan-Chieh Jackson and Liao, Renjie , booktitle =. 2026 , url =

    2026

  39. [39]

    Advances in Neural Information Processing Systems , volume=

    Textctrl: Diffusion-based scene text editing with prior guidance control , author=. Advances in Neural Information Processing Systems , volume=

  40. [40]

    arXiv preprint arXiv:2504.21682 , year=

    Visual text processing: A comprehensive review and unified evaluation , author=. arXiv preprint arXiv:2504.21682 , year=

    Pith/arXiv arXiv

  41. [41]

    arXiv preprint arXiv:2605.14708 , year=

    StyleTextGen: Style-Conditioned Multilingual Scene Text Generation , author=. arXiv preprint arXiv:2605.14708 , year=

    Pith/arXiv arXiv