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arxiv: 2605.16399 · v1 · pith:FAQNVKWJnew · submitted 2026-05-12 · 💻 cs.CV · cs.LG

Stable and Near-Reversible Diffusion ODE Solvers for Image Editing

Barbora Barancikova , Daniil Shmelev , Cristopher Salvi This is my paper

Pith reviewed 2026-05-20 22:00 UTC · model grok-4.3

classification 💻 cs.CV cs.LG
keywords diffusion inversionimage editingODE solversRunge-Kutta methodsreversibilityvector-field smoothingstabilitytext-guided editing
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The pith

Near-reversible Runge-Kutta methods with vector-field smoothing stabilize diffusion inversion for large image edits.

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

This paper examines the limitations of exactly reversible ODE solvers in diffusion model inversion for text-guided image editing. It finds that perfect reversibility creates numerical instabilities that degrade quality when edits involve larger semantic or visual changes, forcing a trade-off between background preservation and prompt alignment. The authors propose near-reversible Runge-Kutta methods paired with vector-field smoothing as a practical fix. This combination delivers higher edit fidelity and greater stability while keeping most of the background-preservation advantages of reversible schemes.

Core claim

Algebraically reversible ODE solvers eliminate inversion error for diffusion-based image editing but exhibit instabilities under large edits that cause sharp quality drops. Near-reversible Runge-Kutta methods combined with vector-field smoothing mitigate these instabilities, improving edit fidelity and remaining stable for substantial changes while largely retaining the background-preservation benefits of reversible solvers.

What carries the argument

Near-reversible Runge-Kutta methods for diffusion ODEs that relax exact reversibility to improve numerical stability, used together with a vector-field smoothing strategy applied during inversion.

If this is right

  • Large semantic or visual edits become feasible without the previous sharp drops in output quality.
  • Text-guided edits achieve stronger alignment with the input prompt.
  • Background elements remain largely unchanged, similar to results from reversible solvers.
  • The method works with standard diffusion models for practical editing pipelines.

Where Pith is reading between the lines

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

  • These solvers could extend to video editing to reduce temporal inconsistencies across frames.
  • The degree of near-reversibility might be tuned automatically based on edit size for optimal results.
  • Similar smoothing techniques could stabilize inversion in other ODE-based generative tasks.

Load-bearing premise

The instabilities seen with exactly reversible solvers are mainly numerical and can be fixed by relaxing exact reversibility without creating new problems that cancel the gains.

What would settle it

Experiments on diverse large-edit cases that still show instabilities, quality drops, or loss of background preservation with the near-reversible approach would disprove the claimed benefits.

Figures

Figures reproduced from arXiv: 2605.16399 by Barbora Barancikova, Cristopher Salvi, Daniil Shmelev.

Figure 1
Figure 1. Figure 1: Qualitative comparison of (near) reversible solvers on image editing tasks. (a) Standard PIE-Bench editing tasks (Sec￾tion 5.2). Here, we use Smooth Diffusion for BELM, EDICT, and EES. (b) PIE-Bench images with large prompt deviations (Sec￾tion 5.3) and greyscale conversion (Section E.3). Here, we use Smooth Diffusion for all methods. See extended grids in Figures 9, 15, 17 and 18. In this setting, the cho… view at source ↗
Figure 3
Figure 3. Figure 3: Qualitative editing comparison for EES under Stable Diffusion 1.5 (top) and Smooth Diffusion (bottom). Smooth Dif￾fusion improves background preservation (e.g., the fence) while maintaining the intended edit. See [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Prompt alignment (CLIP similarity of the edited region) versus background preservation (LPIPS outside the edit mask) on PIE-Bench. Reversible and near-reversible solvers lie on the trade￾off curve between background similarity and edit quality [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Example comparing DDIM and EES under the same edit. DDIM is worse at preserving background. See [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (Shmelev et al., 2025, [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Effect of each smoothing method on PIE-Bench metrics for each solver (arrows indicate the shift from no smoothing to the corresponding smoothing method). From top-left to bottom-right: Smooth Diffusion, Smooth Diffusion + Proximal Guidance, NPI, and Proximal Guidance. We are seeking methods in the top right corner [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Ablations over solver configuration on the random images category of PIE-Bench. Each panel plots edit prompt alignment against background preservation for EES(2,5), EES(2,7), and Reversible Heun. We vary three separate dimensions: ODE parametrisation (marker shape: original (25), half logSNR in ϵ (26) and x (27), sigma (28)), discretisation variable (text label t/λ indicates uniform steps in that variable)… view at source ↗
Figure 9
Figure 9. Figure 9: Extended grid for examples in [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Equivalent of [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Equivalent of [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The impact of the BDIA hyperparameter γ and the EDICT hyperparameter p on the large-prompt-deviations task in Section 5.3. We use Smooth Diffusion for all samples. E.8. Varying the Guidance Scale In [PITH_FULL_IMAGE:figures/full_fig_p025_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Empirical distribution of the inverted terminal latents xT for the image in [PITH_FULL_IMAGE:figures/full_fig_p026_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Equivalent of [PITH_FULL_IMAGE:figures/full_fig_p027_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Extended grid for examples in [PITH_FULL_IMAGE:figures/full_fig_p028_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Extended grid for [PITH_FULL_IMAGE:figures/full_fig_p029_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Extended grid for examples in [PITH_FULL_IMAGE:figures/full_fig_p029_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Extended grid for examples in [PITH_FULL_IMAGE:figures/full_fig_p030_18.png] view at source ↗
read the original abstract

The inversion of diffusion models plays a central role in image editing. Algebraically reversible ODE solvers provide an appealing approach to diffusion inversion for text-guided image editing, by eliminating the inversion error inherent in DDIM-based editing pipelines. However, empirical results indicate that reversibility alone is insufficient. As edits require larger semantic or visual changes, reversible diffusion solvers often exhibit instabilities and suffer sharp drops in output quality. In this paper, we show that the trade-off between exact reversibility and numerical stability manifests empirically as a trade-off between background preservation and prompt alignment in image editing. We then investigate the use of near-reversible Runge-Kutta methods as a more stable alternative to exactly reversible diffusion schemes. When combined with a vector-field smoothing strategy, the resulting approach improves edit fidelity, remains stable under large edits, and largely retains the background-preservation benefits of reversible solvers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that exactly reversible diffusion ODE solvers, while eliminating inversion error and preserving background in text-guided image editing, become unstable for large semantic edits; it proposes near-reversible Runge-Kutta methods plus vector-field smoothing as a practical alternative that improves edit fidelity and stability while largely retaining the background-preservation benefits.

Significance. If the empirical trade-off between exact reversibility and stability is validated with quantitative evidence, the work would supply a concrete engineering improvement for diffusion inversion pipelines that balances fidelity and robustness without requiring new model training.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (Experiments): the central claim that near-reversible RK methods plus smoothing resolve instabilities rests on unshown quantitative metrics, ablation tables, or diagnostic plots separating numerical solver error from latent-space sensitivity to small trajectory deviations; without these the improvement cannot be assessed as load-bearing.
  2. [§3] §3 (Method): the assumption that observed instabilities are primarily numerical (and therefore fixable by relaxing exact reversibility) is not tested against the alternative that large prompt-driven edits amplify any inversion error through the diffusion ODE's inherent sensitivity; a controlled diagnostic (e.g., fixed prompt, varying solver tolerance) is needed to confirm the root cause.
minor comments (2)
  1. [§4.2] Figure captions and §4.2: add explicit definitions or references for the background-preservation and prompt-alignment metrics used in the qualitative comparisons.
  2. [§2] Notation in §2: the precise mathematical definition of 'near-reversibility' (e.g., the tolerance or step-size relaxation relative to exact reversibility) should be stated as an equation rather than described only in prose.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and have revised the manuscript to incorporate additional quantitative support and diagnostics where feasible.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Experiments): the central claim that near-reversible RK methods plus smoothing resolve instabilities rests on unshown quantitative metrics, ablation tables, or diagnostic plots separating numerical solver error from latent-space sensitivity to small trajectory deviations; without these the improvement cannot be assessed as load-bearing.

    Authors: We agree that stronger quantitative backing is needed to substantiate the central claim. The revised manuscript now includes quantitative metrics such as prompt alignment (CLIP similarity) and background preservation (PSNR and LPIPS on unchanged regions) evaluated across a range of edit strengths. We have added ablation tables comparing exact reversible solvers against near-reversible RK variants with and without vector-field smoothing. Diagnostic plots showing error accumulation and sensitivity to trajectory perturbations have also been included in the updated Section 4 and a new appendix to separate numerical solver effects from latent-space dynamics. revision: yes

  2. Referee: [§3] §3 (Method): the assumption that observed instabilities are primarily numerical (and therefore fixable by relaxing exact reversibility) is not tested against the alternative that large prompt-driven edits amplify any inversion error through the diffusion ODE's inherent sensitivity; a controlled diagnostic (e.g., fixed prompt, varying solver tolerance) is needed to confirm the root cause.

    Authors: We acknowledge the importance of isolating the root cause. In the revised Section 3, we have added a controlled diagnostic experiment that fixes the target prompt and systematically varies solver tolerance (including step size and integration order) during inversion and editing. The results indicate that instabilities scale with reduced numerical precision even under fixed prompts, supporting a substantial numerical contribution. We also discuss the interaction with the ODE's inherent sensitivity to prompt-driven changes and how the proposed smoothing strategy addresses both aspects. While perfect isolation of factors remains difficult due to their coupling in the diffusion process, the new experiment provides direct evidence for the role of numerical stability. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical engineering proposal remains self-contained

full rationale

The paper's central contribution is an empirical observation that exact reversibility in diffusion ODE solvers trades off against numerical stability during large edits, followed by the proposal to use near-reversible Runge-Kutta methods plus vector-field smoothing. No derivation chain reduces any claimed result to a fitted parameter, self-defined quantity, or self-citation loop. The abstract explicitly frames the trade-off as manifesting 'empirically' and the solution as an 'investigation' of alternatives, without algebraic identities or uniqueness theorems that loop back to the inputs. The approach is presented as an engineering choice validated by results rather than a first-principles identity equivalent to its own assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the unstated premise that numerical stability can be traded for exact reversibility in a controlled way; no free parameters, axioms, or invented entities are explicitly introduced in the abstract.

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Reference graph

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