One implicit DDIM inversion step is the cheapest probe of whether a pretrained diffusion model encodes local manifold geometry. It is the stationarity condition of an explicit potential, $x-G(x)=\nablaΨ_t(x)$, strongly convex at the Bayes limit with modulus exactly $e^{-h_t}$ for the step's log-SNR gap $h_t$ $-$ for every data law, schedule and point, with no manifold, reach or unimodality hypothesis. Three consequences must be kept apart. (i) The solution is unique at the Bayes limit; a second one requires the trained score to violate the posterior-covariance bound by $1/(1-e^{-h_t})$, a hypothesis-free certificate of model error; the same bound makes contraction a schedule constant, $ρ_g^{\star}=1-e^{-h_t}<0.326$ throughout the standard DDPM schedule. (ii) The solver can still fail: Picard iteration is unit-step gradient descent on $Ψ_t$, unstable wherever $λ_{\max}(\nabla^2Ψ_t)>2$, so oscillation certifies nothing; damping below $2/λ_{\max}$ cures it. (iii) The geometry lives in the convergence domain: on the scale-free depth $w=rκ_{\max}$ the oscillation shell sits at $w=\tfrac12$, schedule-free, and the divergence shell at $w=1/(1+ρ_g^{\star})$, with a measured finite-noise correction in $\|\mathrm{II}\|^2$. Exact scores reproduce both to within $0.54\%$ on three classes; no trained score we probe shows a shell $-$ a derived limitation, not a null result: the Fermi window conflicts with the model's own training support by $3.6$-$5.6\times$, and the trained Hessian-Lipschitz constant is $2$-$12\%$ of the curvature the law reads, $0$ on a ReLU net. Finally the unconditional ceiling $σ_tλ_{\max}(\mathrm{sym}\,J)\le1$, from $\mathrm{Cov}(x_0\mid x_t)\succeq0$ alone, holds for the exact score to $3\times10^{-7}$ but is violated in all DDPM CIFAR-10/CelebA-HQ-256 settings, by $1.26$-$4.66\times$.
Although text-to-image diffusion models exhibit remarkable generative power, concept erasure techniques are essential for preventing harmful content. Existing adversarial probes evaluate these methods by testing whether erased concepts can still be recovered. However, existing erasure and probe methods remain largely text-centric, focusing on whether the text-to-image mapping is severed while overlooking whether the corresponding visual knowledge remains. To investigate this question from a visual perspective, we leverage diffusion inversion to probe whether a generative trajectory can reconstruct visual instances of an erased concept. Under a null-text condition, standard inversion avoids the textual pathway but amplifies approximation errors, hindering faithful trajectory recovery. To address this challenge, we introduce TINA+, a diffusion-consistent Text-free INversion Attack equipped with optimization-based inversion. We also find that unconstrained diffusion inversion may discover spurious trajectories, even allowing a randomly initialized diffusion model to reconstruct the target concept. Such trajectories may falsely indicate residual visual knowledge. TINA+ therefore introduces Diffusion-Consistent Trajectory Regularization to suppress this failure mode. By penalizing trajectories that fall far below the expected marginal energy evolution of diffusion, TINA+ suppresses spurious inversion paths while preserving its ability to recover erased concepts. Experiments across twelve erasure methods, four concept-erasure tasks, and different model architectures demonstrate that TINA+ reliably probes residual visual knowledge through diffusion-consistent visual trajectories. These results provide stronger evidence that current methods often obscure concepts by severing text-image links rather than eliminating the underlying visual knowledge.
Graph Neural Networks (GNNs) achieve strong predictive performance on graph-structured data across domains such as chemistry, biology, and network analysis, yet they provide no intrinsic explanation of their predictions. This limits their adoption in high-stakes and safety-critical settings. Counterfactual explanations address this by revealing the minimal structural modifications that would change a model's prediction. On graphs, however, such a modification is hard to produce. The search space is discrete and combinatorial, and a valid answer must respect categorical node and edge types together with domain rules such as chemical valency in the case of molecular graphs. Existing explainers give up one of two things. Either edits are not held on the data manifold, or the search does not span the full edit space. We propose Graph Diffusion Counterfactual Explanation via Inversion (GDCE-I), which gives up neither. A discrete denoising diffusion model with a novel discrete inversion scheme enables distribution-aware edits leveraging the whole domain edit space. We further address the incomplete and inconsistent evaluation of graph counterfactuals by deriving a framework of explanation desiderata and applying it to every method under one shared protocol. Across four benchmarks, GDCE-I outperforms related work by a large margin on the defined framework. For the molecular domain, we further qualitatively show that GDCE-I attains interpretable in-distribution solutions.
Yongseong Park, Joeun Kim, HoEun Kim +1cs.CV cs.IT
Real-image diffusion inversion is governed by a tight quality-cost trade-off, with costs incurred in computation, storage, or per-image optimization. We study this trade-off through the forward Gaussian noise anchor that defines a diffusion trajectory and isolate two mechanisms behind effective stored-noise inversion. First, diffusion noise exhibits an element-wise compression asymmetry: int8 full-dimensional anchors preserve reconstruction, whereas low-dimensional subspace summaries are much less reliable, often collapsing even at comparable or smaller payloads; the element-wise over subspace ordering persists across five stored-noise inversion methods. Second, inversion is trajectory-bound and score-prior coupled: the matched forward anchor and a trained score network are both necessary, arguing against a purely algebraic-identity explanation. Together, these findings specify what to store and how to use it. They lead to Noise-Anchored Reverse Correction (NARC), a training-free inversion primitive that stores a single int8 latent anchor and reuses it with a fixed, noise-level-dependent anchor-weight schedule: strong anchoring when the reverse trajectory is noise-dominated, then relaxed anchoring as image detail emerges. On PIE-Bench++ with Stable Diffusion 1.5, NARC outperforms five modern non-exact baselines and improves PSNR by +3.24 dB over PnP DirectInv while using about 400x less inversion storage than PnP DirectInv. The compression asymmetry, anchor specificity, and editing plug-in also transfer to SDXL 1024^2.
Text-guided diffusion inversion is central to image editing, where an image is mapped to an initial latent and then edited by replaying the denoising process under a modified prompt. In practice, however, inversion is often performed with a lower classifier-free guidance(CFG) scale than the one used for generation or editing. This mismatch is empirically useful but leaves a basic question unresolved: when a target image is generated by a high-CFG trajectory, when can that trajectory actually be inverted? We study this question in a controlled generation--inversion--reconstruction setting, where the true initial latent and denoising trajectory are known. Using prompts taken from an existing diffusion-editing benchmark, we generate images under high CFG and reconstruct them with fixed-point inversion using the same prompt and guidance setting. The results reveal three types of prompt-level reconstruction behavior: easy prompts that reconstruct for most initial latents, hard prompts that fail for most initial latents, and intermediate prompts whose success depends on the prompt--latent pairing. To analyze the generation side, we define prompt pressure, a step-wise measure of how strongly CFG moves the denoising update away from the unconditional trajectory. Total pressure correlates with reconstruction quality and separates easy from hard prompts, but it does not explain the success or failure of intermediate prompt--latent pairs. Text-side analyses further show that the main visual subject and wording can change inversion difficulty. Finally, we evaluate a compact trajectory-consistency intervention that relaxes guidance only at locally unstable inverse steps. This diagnostic check improves reconstruction and Prompt-to-Prompt editing in our controlled setting, supporting the view that high-CFG inversion failure requires local, trajectory-aware analysis.
Diffusion inversion, which maps images back to the Gaussian latent space of a diffusion model, is a critical task for image reconstruction and editing. While DDIM enables fast deterministic inversion, it inherently introduces deviations that accumulate into noticeable inversion errors. Existing methods often address this by solving a fixed-point problem but largely overlook how the selection of the diffusion timestep in the noise scheduler influences inversion fidelity. In this work, we reveal that the deviation scale in diffusion inversion is strongly dependent on the timestep size, and exhibits a parabolic trend, with larger errors concentrated at both small and large timesteps. Based on this finding, we propose a simple yet effective nonuniform timestep scheduler that integrates a global rescaling with a local dynamic programming based rescheduling, enabling a strategic allocation of computational effort that minimizes the overall inversion error and preserves higher inversion accuracy. Our method serves as an off-the-shelf enhancement for existing inversion techniques and requires no extra parameters or computational overhead. Through extensive experiments, we verify that integrating our scheduler consistently boosts the performance of existing inversion methods, achieving superior results in image reconstruction and editing.
Text-guided diffusion models have become effective tools for real-image visual editing, where the edited image must follow a target instruction while preserving editing-irrelevant structure. Most training-free editors rely on inversion: a source image is mapped to a noisy latent trajectory and the terminal latent is reused for target-prompt denoising. This reuse is useful for preservation, but it also couples source reconstruction and target editing. The resulting trajectory mismatch may either damage background/layout details or over-constrain the intended edit. This paper presents Consistent-Inversion, a training-free reverse consistency guidance framework for structure-preserving visual editing. Instead of treating the inverted source latent as a fixed initialization, Consistent-Inversion checks whether an intermediate target trajectory can be reversed toward the source inversion trajectory under the source prompt. To make this check well-defined, we construct an auxiliary target-side noise representation, perform source-guided reverse denoising, and use the resulting reverse consistency discrepancy as a correction signal for selected early target denoising steps. The method does not update model parameters, is compatible with inversion-based editors, and introduces only a small inference overhead when applied sparsely. Experiments on PIE-Bench show that Consistent-Inversion improves background and structural fidelity under a unified SD3.5 protocol while maintaining target-prompt alignment, and compatibility experiments further verify the same correction principle on classical Stable-Diffusion inversion pipelines.
Recent advances in diffusion models have enabled high-quality image generation, leading to increasing demand for post-generation editing that modifies local regions while preserving global structure. Achieving such flexible and precise editing requires a high-quality starting point, a latent representation that provides both the freedom needed for diverse modifications and the precision required for fine-grained, region-specific control. However, existing inversion-based approaches such as DDIM inversion often yield unsatisfactory starting latents, resulting in degraded edit fidelity and structural inconsistency. Ideally, the most suitable editing anchor should be the original latent used during the generation process, as it inherently captures the scene's structure and semantics. Yet, storing this latent for every generated image is impractical due to massive storage and retrieval costs. To address this challenge, we propose ResetEdit, a proactive diffusion editing framework that embeds recoverable latent information directly into the generation process. By injecting the discrepancy between the clean and diffused latents into the diffusion trajectory and extracting it during inversion, ResetEdit reconstructs a resettable latent that closely approximates the true starting state. Additionally, a lightweight latent optimization module compensates for reconstruction bias caused by VAE asymmetry. Built upon Stable Diffusion, ResetEdit integrates seamlessly with existing tuning-free editing methods and consistently outperforms state-of-the-art baselines in both controllability and visual fidelity.