Support-guided OOD Removal with Diffusion

1 INTRODUCTION

• Localized structured corruptions—including watermarks, shadows, and interfering sounds—can make simple noise models inadequate, while paired examples or a model for every corruption may be impractical.Corruptions may affect a limited spatial region or a short temporal segment.Source: §1 · p. 1
• SORD replaces statistical knowledge of the corruption distribution with structural knowledge of where or when corruption occurs, which may be easier to identify than its distribution.The approach assumes the corruption support is known.Source: §1 · p. 2
• Across image and audio settings, SORD is competitive with specialized methods using corruption-specific training data or priors, while corruption-specific supervision remains advantageous when test corruptions match training.Comparisons include posterior-sampling methods using the same clean-signal prior and support, supervised restoration, and multi-source diffusion models.Source: §1 · p. 2
• SORD requires only a corruption-support mask and a clean-signal diffusion model, rather than paired examples or a model of the corruption distribution.The method treats localized corruptions as out of distribution and alternates between explaining corrupted measurements and reconstructing a signal consistent with the clean prior and trusted observations.Source: §1 · p. 2

Diffusion priors for inverse problems

• Diffusion-prior inverse-problem methods typically use a specified observation model and known or modeled noise likelihood, unlike localized structured corruptions with unknown parametric models.Examples of likelihoods include Gaussian and Poisson noise.Source: §2 · p. 3

Corruption-specific image restoration

• Corruption-specific image-restoration methods target watermarks or shadows but require paired clean and corrupted images and specialize to particular corruption types.Examples include supervised learning, conditional diffusion, and attention-based models.Source: §2 · p. 3

Generative priors for source separation

• Source-separation methods learn priors for clean signals and anticipated corruption or source classes, whereas SORD assumes a prior only for the desired clean signal.Examples include separate image and noise diffusion priors and audio models for fixed musical-source sets.Source: §2 · p. 3

Localized anomaly and OOD detection

• Localized anomaly-detection methods estimate supports of anomalous regions; SORD assumes access to that support and uses it to recover the underlying clean signal.Prior approaches use feature-space deviations, learned anomaly representations, or diffusion-based representations of inlier data.Source: §2 · p. 3

3 METHOD

• SORD progressively reuses measurements inside the corrupted support because they contain a superposition of clean signal and unknown structured corruption, rather than missing content.The method begins from an inpainting estimate conditioned on uncorrupted measurements.Source: §3 · pp. 3–5
• The procedure initializes with inpainting, then alternates signal–corruption decomposition and measurement-consistency updates with diffusion-prior refinement.The prior refinement follows a noise schedule, and SORD reports stable performance across a wide range of schedules.Source: §3 · pp. 3, 5
• SORD estimates uncertainty from variation across diffusion samples and uses it both to set the refinement scale and to determine when to stop.It returns the mean of independent clean-signal hypotheses when uncertainty stops decreasing sufficiently, or stops at a maximum iteration count.Source: §3 · pp. 4–5
• Residuals can mix true corruption with clean-signal estimation errors, so SORD refines estimated corruption using a diffusion denoiser at an adaptive scale tied to uncertainty.The refinement uses a diffusion model trained on the signal class rather than the corruption class.Source: §3 · p. 5

4 EXPERIMENTS

• SORD beats both SGM variants, is generally more robust to out-of-vocabulary audio interferers, remains competitive on watermarks, and matches ShadowDiffusion on shadows, where ShadowFormer is stronger.MSDM can outperform SORD for some target instruments when the interferer is modeled.Source: §4.1 · p. 6, §4.2 · p. 6, §4.3 · p. 8

4.1 ADDITIVE LOCALIZED STRUCTURED IMAGE CORRUPTIONS

• CelebA tests add MNIST digits, natural-image patches, and CIFAR-10 patches to a clean-image prior; evaluated Gaussian DPS approximations were inadequate for these structured corruptions.SORD also outperformed SGM variants that used separate clean-image and corruption priors, including a mask-informed variant.Source: §4.1 · p. 6

4.2 ADDITIVE LOCALIZED AUDIO INTERFERENCE

• Audio tests use Slakh piano clips with a known half-clip interference window, varying interferer vocabulary and signal-to-interference ratio.SIR levels span 0–5 dB, with an additional default unnormalized mixture setting.Source: §4.2 · p. 6

4.3 WATERMARK REMOVAL

• Watermark tests span CLWD, synthetic FFHQ, and Imagenette images, while withholding the true pixel-wise opacity map despite assuming alpha compositing.Under this model mismatch, SORD is competitive with, but does not always outperform, paired-data watermark baselines.Source: §4.3 · pp. 6, 8

4.4 SHADOW REMOVAL

• For multiplicative shadows, SORD applies measurement-consistency updates in log-intensity space but keeps clean-image diffusion in image space.ISTD shadow and shadow-free targets come from separate camera captures; FFHQ and Imagenette are also tested with synthetic ISTD shadows.Source: §4.4 · pp. 8–9

4.5 ABLATION AND SENSITIVITY STUDIES

• Ablations examine sample count, noise schedule, diffusion sampler and cost, corruption-model choice, imperfect masks, and diffusion residual refinement.The supplied passage describes the study areas but does not report their outcomes.Source: §4.5 · p. 9

• Across image and audio tasks, SORD improves over discarding corrupted measurements and is competitive with specialized methods using corruption-specific data or priors.Source: §5 · p. 9
• When a corruption class is known and well represented in training data, methods that explicitly model it can retain an advantage.Source: §5 · p. 9
• SORD is particularly useful when corruption is unexpected or difficult to model, but it relies on knowing the corruption support.Source: §5 · p. 9
• Overestimating the support tends to degrade performance gracefully, whereas leaving corrupted pixels outside it can be substantially more harmful because they are treated as trustworthy.Source: §5 · p. 9

Localized Structured Corruptions

• Image-patch benchmarks use 100 CelebA test images at 64 × 64, with 32 × 32 natural-image patches or randomly sized CIFAR-10 patches, and SORD uses K = 32 samples and up to six refinement iterations.Source: §A.1 · p. 13
• Image comparisons include DPS inpainting and Gaussian-likelihood variants using the same clean prior, plus a two-prior SGM model trained on synthetic corruption examples.Source: §A.1 · p. 13

Localized Audio Interference

• Audio clips are 10 seconds at 22.05 kHz, with one interfering source in a provided contiguous window covering half the clip; SORD uses K = 64 samples.Source: §A.1 · p. 13

Watermark Removal

• Watermark evaluation covers FFHQ and Imagenette composites using 12 logos and CLWD test images with 40 logos; supports average about 3% and 14% of the image, respectively.Source: §A.1 · p. 13
• Clean-image priors include off-the-shelf ADM models and a CLWD-finetuned EDM2 model, while SLBR uses paired training data and PatchWiper predicts its own watermark support.Source: §A.1 · p. 13

A.1 EXPERIMENT DETAILS

• Table 3 reports corrupted-region PSNR (dB), as mean ± standard deviation over 25 images per benchmark, for SORD's sample-count ablation.Source: Table 3 · p. 14

Shadow Removal

• The ISTD benchmark uses 100 real test shadows at 64 × 64, with the input matched to the shadow-free target outside the declared support, which averages about 17% of the image.Source: K Natural patch MNIST digit CIFAR-10… · p. 14
• Cross-domain tests apply 25 real ISTD shadow fields to held-out FFHQ and Imagenette images at 256 × 256, using their clean-image priors without shadow-specific training on those domains.Source: K Natural patch MNIST digit CIFAR-10… · p. 14

A.2 EFFECT OF THE NUMBER OF SAMPLES

• 24.84 dB corrupted-region PSNR at K = 32, averaged over five image benchmarks, compared with 21.37 dB at K = 2.Source: §A.2 · p. 14
• Increasing K generally improves final reconstruction quality, but the improvement largely saturates beyond K = 32.Source: §A.2 · p. 14
• K controls both the diversity of initial inpainting hypotheses and estimation of ensemble spread σ⋆, motivating K = 32 as the default trade-off between stability and computation.Source: §A.2 · p. 14

A.3 SAMPLING COST

• The faster-sampler test changes only the x-refinement step, leaving the inpainting initialization and n-refinement fixed.The initialization is the K-sample inpainting initialization.Source: §A.3 · p. 14
• Reducing the number of x-refinement steps did not significantly affect final results.Source: §A.3 · p. 14
• Watermark-removal experiments using the ground-truth opacity map are labeled “declared α.”Source: §A.3 · p. 14

A.4 ROBUSTNESS TO IMPERFECT CORRUPTION MASKS

• The sensitivity study perturbs the true support by dilation, erosion, and spatial shifts, evaluating PSNR over the true corrupted region.The supplied-mask/true-mask IoU is also reported.Source: §A.4 · p. 14, Table 5 · p. 15
• Mask dilation causes gradual degradation as extra clean pixels are treated as unknown and reconstructed by the diffusion prior.Source: §A.4 · p. 14
• Underestimating the support can lock contamination into the reconstruction because SORD preserves observations outside the supplied mask.Eroding the mask by one pixel can substantially decrease mean PSNR.Source: §A.4 · p. 15
• Over-covering the corruption is substantially safer than leaving corrupted pixels outside the mask.Source: §A.4 · p. 15
• CLWD watermark removal is less sensitive to small erosions because mask-boundary pixels often have small or near-zero opacity.In this experiment, a one-pixel eroded mask performed comparably to, and slightly above, the exact mask.Source: §A.4 · p. 15
• Qualitative examples show dilation regenerating nearby clean content, while erosion or misalignment leaves residual corruption outside the modifiable region.Source: §A.4 · p. 15, Figure 4 · p. 18