Support-guided OOD Removal with Diffusion

Alireza Kheirandish; Sara Fridovich-Keil

cs.CVOct 23, 2026

Support-guided OOD Removal with Diffusion

Authors: Alireza Kheirandish, Sara Fridovich-Keil

Organizations: Georgia Institute of Technology, Atlanta, GA, USA

Abstract

Many real-world signals are corrupted by localized, structured perturbations whose distribution is unknown: an intermittent background noise in a music recording, a watermark stamped on a photograph, a cast shadow. We study the task of recovering a clean signal $x$ from an observation $y$ containing such a localized out-of-distribution (OOD) corruption. We propose Support-guided OOD Removal with Diffusion, SORD, an iterative algorithm to recover $x$ using only two ingredients: a binary map of the corruption support and a single diffusion model pretrained on clean signals. SORD does not require any paired data or any statistical model of the corruption. We evaluate SORD on natural images and human faces with spatially localized corruptions including handwritten digits, other images, watermarks, and shadows, as well as audio recordings of different musical instruments with temporally localized corruptions including other instruments and human speech. SORD is competitive with, and often outperforms, posterior-sampling inpainting given the same diffusion prior and the same mask, source-separation baselines that require a separate diffusion model for each source, and, on several benchmarks, supervised networks trained on paired clean and corrupted signals. The code is released here: https://github.com/voilalab/SORD.

Figures & tables

Figure 2: Visual results on localized image corruption removal. Each pair of rows corresponds to a different restoration setting: Rows 1–6 respectively show localized MNIST-digit, natural-image patch, and CIFAR-10 patch corruptions on CelebA faces. For those settings, Baseline 1 is Stevens et al. (2025) , using separate CelebA and corruption-patch diffusion priors, while Baseline 2 is its mask-projected variant. Rows 7–8 show watermark removal on CLWD, with PatchWiper ( Mo et al., 2025 ) as Baseline 1 and SLBR ( Liang et al., 2021 ) as Baseline 2. Rows 9–10 show shadow removal on ISTD, with ShadowDiffusion ( Guo et al., 2023b ) as Baseline 1 and ShadowFormer ( Guo et al., 2023a ) as Baseline 2. Red contours or bounding boxes indicate the known corruption support $\Omega$ . Numbers below the reconstructions denote PSNR computed only over $\Omega$ .

Image Corruption	Input	DPS Inpaint	DPS $\boldsymbol{\mu=\mu_{n}}$	DPS $\boldsymbol{\mu=0}$	SGM 2 priors	SGM 2 priors + mask	$\mathrm{SORD}$
MNIST	$12.09$ $\pm\,2.47$	$19.85$ $\pm\,2.77$	$11.06$ $\pm\,1.18$	$11.91$ $\pm\,2.17$	$25.78$ $\pm\,3.42$	$22.51$ $\pm\,3.89$	$\mathbf{27.16}$ $\pm\,2.04$
Natural patch	$9.37$ $\pm\,1.62$	$16.84$ $\pm\,2.94$	$15.74$ $\pm\,2.75$	$9.32$ $\pm\,1.58$	$18.92$ $\pm\,7.15$	$19.38$ $\pm\,6.38$	$\mathbf{21.96}$ $\pm\,2.32$
CIFAR-10 patch	$7.92$ $\pm\,1.90$	$17.28$ $\pm\,3.92$	$14.87$ $\pm\,2.18$	$7.83$ $\pm\,1.89$	$14.36$ $\pm\,3.93$	$15.34$ $\pm\,4.16$	$\mathbf{22.05}$ $\pm\,3.44$
Audio Interferer	Mix	$\boldsymbol{N}$	DPS Inpaint	DPS $\boldsymbol{\mu=\mu_{n}}$	DPS $\boldsymbol{\mu=0}$	MSDM	$\mathrm{SORD}$
IV instrument	SIR $0$	$60$	$-0.34$ $\pm\,6.17$	$-0.01$ $\pm\,0.05$	$-0.06$ $\pm\,0.43$	$\mathbf{5.32}$ $\pm\,7.64$	$1.12$ $\pm\,5.11$
IV instrument	SIR $5$	$60$	$-0.12$ $\pm\,5.67$	$0.00$ $\pm\,0.07$	$0.01$ $\pm\,0.09$	$1.40$ $\pm\,6.85$	$\mathbf{2.74}$ $\pm\,6.23$

Table 1: Localized structured corruption removal across image and audio domains. Image results report PSNR (dB) within

\Omega

100

CelebA images at

64\times 64

resolution. Audio results report SI-SDRi improvement on

\Omega

, and the target is piano for all of the audio experiments. All values are mean

\pm

standard deviation. IV and OOV denote in-vocabulary and out-of-vocabulary interferers for MSDM, respectively; for speech, IV uses MSDM augmented with a speech prior, while OOV uses the original four-source MSDM without a speech prior. The setting

g=1

denotes the unnormalized mixture. SGM and MSDM use explicit contaminant/source priors, whereas

\mathrm{SORD}

uses only the clean source prior and corruption support

\Omega

. DPS

\mu=\mu_{n}

uses the oracle per-image mean of the true corruption on its support. The highest mean in each row is shown in bold .

N

denotes the number of evaluated mixtures.

Benchmark	Input	DPS Inpaint	DPS $\boldsymbol{\mu=\mu_{n}}$	DPS $\boldsymbol{\mu=0}$	SLBR	PatchWiper	$\mathrm{SORD}$
FFHQ	$13.49\pm 3.20$	$27.13\pm 3.81$	$18.80\pm 5.11$	$14.35\pm 3.89$	$18.90\pm 5.10$	$23.44\pm 5.59$	$\mathbf{27.80\pm 3.50}$
CLWD	$22.55\pm 5.33$	$17.14\pm 4.74$	$24.26\pm 5.15$	$22.73\pm 5.30$	$\mathbf{31.55\pm 4.47}$	$31.37\pm 6.84$	$25.09\pm 4.87$
Imagenette	$13.64\pm 4.30$	$24.81\pm 7.56$	$19.63\pm 7.18$	$14.56\pm 4.61$	$21.66\pm 5.08$	$21.79\pm 6.89$	$\mathbf{26.43\pm 6.56}$
Benchmark	Input	DPS Inpaint	DPS $\boldsymbol{\mu=\mu_{n}}$	DPS $\boldsymbol{\mu=0}$	Shadow Diffusion	Shadow Former	$\mathrm{SORD}$
ISTD	$14.48\pm 3.70$	$27.44\pm 7.08$	$27.60\pm 4.21$	$14.57\pm 3.77$	$\mathbf{30.60\pm 4.93}$	$30.49\pm 5.18$	$29.10\pm 5.55$
FFHQ	$14.89\pm 4.13$	$17.39\pm 3.85$	$19.85\pm 3.80$	$14.83\pm 4.09$	$19.15\pm 3.23$	$\mathbf{23.29\pm 2.89}$	$20.34\pm 4.19$

Table 2: Localized structured corruption removal on watermark and shadow benchmarks. Task-specific baselines use dedicated training data or corruption models, whereas

\mathrm{SORD}{}

uses only the clean-image prior and the known corruption support. DPS

\mu=\mu_{n}

uses the oracle per-image mean of the true corruption on the support. Highest mean in each row is shown in bold .

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

$K$	Natural patch	MNIST digit	CIFAR-10 patch	CLWD watermark	ISTD shadow
$2$	$18.26$ $\pm\,2.37$	$24.30$ $\pm\,2.50$	$17.44$ $\pm\,2.64$	$23.39$ $\pm\,3.72$	$27.45$ $\pm\,6.99$
$4$	$20.42$ $\pm\,2.28$	$25.46$ $\pm\,2.03$	$20.07$ $\pm\,2.96$	$23.63$ $\pm\,3.93$	$28.77$ $\pm\,6.06$
$8$	$21.74$ $\pm\,2.18$	$26.54$ $\pm\,1.81$	$21.36$ $\pm\,3.20$	$24.41$ $\pm\,3.81$	$29.60$ $\pm\,6.19$
$16$	$22.22$ $\pm\,2.08$	$27.09$ $\pm\,1.48$	$21.91$ $\pm\,3.54$	$24.68$ $\pm\,3.87$	$30.08$ $\pm\,5.99$
$\mathbf{32}$ (default)	$22.52$ $\pm\,2.03$	$27.28$ $\pm\,1.43$	$22.23$ $\pm\,3.41$	$25.04$ $\pm\,3.97$	$\mathbf{30.13}$ $\pm\,6.02$
$64$	$\mathbf{22.54}$ $\pm\,1.84$	$\mathbf{27.40}$ $\pm\,1.44$	$\mathbf{22.41}$ $\pm\,3.43$	$\mathbf{25.06}$ $\pm\,4.19$	$29.98$ $\pm\,6.20$

Appendix

Table 3: Ablation on the number of diffusion samples

K

. Each entry reports corrupted-region PSNR (dB) of

\mathrm{SORD}

as mean

\pm

standard deviation over

25

images per benchmark.

K=1

is not reported because

\sigma^{\star}

is the spread across samples. Best mean in each column is shown in bold .

Bench	$N$	All levels (default)	8 DDIM levels	4 DDIM levels
Natural patch on CelebA	100	$\mathbf{21.96}$ $\pm\,2.33$ [1640]	$\mathbf{21.96}$ $\pm\,2.33$ [1352]	$\mathbf{21.96}$ $\pm\,2.34$ [840]
MNIST digit on CelebA	100	$\mathbf{27.16}$ $\pm\,2.05$ [1190]	$\mathbf{27.16}$ $\pm\,2.05$ [966]	$27.15$ $\pm\,2.04$ [614]
CIFAR-10 patch on CelebA	100	$\mathbf{22.05}$ $\pm\,3.45$ [1640]	$\mathbf{22.05}$ $\pm\,3.45$ [1352]	$\mathbf{22.05}$ $\pm\,3.45$ [840]
CLWD $+$ watermark (declared $\alpha$ )	99	$28.06$ $\pm\,6.48$ [1184]	$28.06$ $\pm\,6.48$ [960]	$\mathbf{28.07}$ $\pm\,6.47$ [608]
PRWD $+$ watermark (declared $\alpha$ )	100	$30.75$ $\pm\,7.73$ [1184]	$30.75$ $\pm\,7.73$ [960]	$\mathbf{30.76}$ $\pm\,7.72$ [608]
FFHQ $+$ watermark (declared $\alpha$ )	25	$\mathbf{30.05}$ $\pm\,3.99$ [416]	$\mathbf{30.05}$ $\pm\,3.99$ [336]	$30.03$ $\pm\,3.98$ [208]

Appendix

Table 4: Number of DDIM steps in the

x

-refinement step. Our main results use the “shipped”

\mathrm{SORD}

variant, which runs the

x

-refinement step following DDIM over every ladder level at or below

\sigma_{m}

(13 levels at the largest noise level). We test computationally cheaper variants that cap the ladder at

8

4

DDIM levels, with everything else unchanged (

K

-sample inpainting initialization). Image rows report corrupted-region PSNR (dB); audio rows report corruption-window SI-SDRi (dB), both as mean

\pm

standard deviation. Brackets report the number of network evaluations per image spent in the alternating loop (

x

-step and

n

-step) excluding the initialization, which is identical across columns. The highest mean in each row is shown in bold .

Benchmark	Exact	Dilate 3 px	Dilate 5 px	Erode 1 px	Shift 2 px
Natural patch	$\mathbf{21.96}$ $\pm\,2.33$	$19.94$ $\pm\,2.53$ $(0.73)$	$18.85$ $\pm\,2.54$ $(0.62)$	$13.84$ $\pm\,2.18$ $(0.88)$	$14.38$ $\pm\,2.08$ $(0.78)$
MNIST digit	$\mathbf{27.16}$ $\pm\,2.05$	$24.40$ $\pm\,2.72$ $(0.59)$	$23.32$ $\pm\,2.90$ $(0.47)$	$17.83$ $\pm\,1.48$ $(0.76)$	$15.20$ $\pm\,2.17$ $(0.60)$
CLWD watermark	$25.09$ $\pm\,4.33$	$23.60$ $\pm\,3.96$ $(0.59)$	$22.39$ $\pm\,3.72$ $(0.47)$	$\mathbf{25.47}$ $\pm\,4.91$ $(0.75)$	$21.14$ $\pm\,4.26$ $(0.61)$
CIFAR-10 patch	$\mathbf{22.05}$ $\pm\,3.45$	$19.53$ $\pm\,3.44$ $(0.69)$	$18.96$ $\pm\,3.47$ $(0.57)$	$12.11$ $\pm\,2.62$ $(0.85)$	$12.36$ $\pm\,2.70$ $(0.74)$

Appendix

Table 5: Robustness to imperfect corruption masks. We perturb the true corruption support using dilation, erosion, and spatial shifts and evaluate PSNR (dB) over the true corrupted region. Values in parentheses report IoU between the perturbed and true masks. The highest mean in each row is shown in bold .

Method	Natural $N=100$	MNIST $N=100$	CIFAR-10 $N=100$	CLWD WM $N=99$	PRWD WM $N=100$	FFHQ WM $N=25$
DM $n$ -step	$\mathbf{21.96}$ $\pm\,2.33$	$\mathbf{27.16}$ $\pm\,2.05$	$\mathbf{22.05}$ $\pm\,3.45$	$\mathbf{24.56}$ $\pm\,4.33$	$\mathbf{23.81}$ $\pm\,5.17$	$26.68$ $\pm\,3.58$
No DM $n$ -step	$20.16$ $\pm\,2.27$	$24.28$ $\pm\,2.36$	$20.40$ $\pm\,3.38$	$22.59$ $\pm\,4.61$	$22.81$ $\pm\,6.32$	$\mathbf{29.22}$ $\pm\,4.08$
Method	Imagenette WM $N=25$	ISTD $N=100$	ISTD on FFHQ $N=25$	ISTD on Imagenette $N=25$	Slakh piano IV+OOV, $N=100$	Slakh guitar IV+OOV, $N=50$
DM $n$ -step	$24.92$ $\pm\,6.49$	$\mathbf{29.10}$ $\pm\,5.55$	$\mathbf{20.34}$ $\pm\,4.19$	$\mathbf{19.05}$ $\pm\,6.50$	$\mathbf{3.31}$ $\pm\,6.75$	$\mathbf{3.46}$ $\pm\,5.14$
No DM $n$ -step	$\mathbf{27.35}$ $\pm\,7.41$	$28.83$ $\pm\,5.76$	$19.81$ $\pm\,3.97$	$17.23$ $\pm\,5.49$	$2.85$ $\pm\,7.31$	$2.78$ $\pm\,5.84$

Appendix

Table 6: Effect of removing the diffusion

n

-step across benchmarks. The default method re-noises the estimated residual to noise level

\sigma^{\star}

and denoises it with the clean-signal diffusion prior; “No DM

n

-step” instead uses the clipped raw residual while keeping all other components unchanged. Image results report PSNR (dB) over the corrupted support, while audio results report in-window SI-SDR (dB), as mean

\pm

standard deviation. Audio experiments use

K=4

and

M=4

for computational efficiency. The highest mean in each column is shown in bold .

Figure 3: Visualization of localized audio interference removal. Each row shows a Slakh piano clip corrupted by a temporally localized interferer within the dashed interval. Columns show the mixture $y$ , the ground-truth interferer, MSDM, $\mathrm{SORD}{}$ using only the clean-piano prior, and the clean target. Rows 1–5 use IV interferers (drums, guitar, bass, and speech), for which MSDM has corresponding source priors, while Rows 6–10 use OOV interferers (strings, organ, reed, brass, and synthesizer pad), for which no matched MSDM prior is available. Values report in-window SI-SDR and, in parentheses, improvement over the input mixture.

$\sigma_{m}$ schedule	Natural	MNIST	CIFAR-10
$0.4\rightarrow 0.1$ , $M=6$	$\mathbf{21.96}\pm 2.33$	$\mathbf{27.16}\pm 2.05$	$\mathbf{22.05}\pm 3.45$
Constant $0.8$	$20.50\pm 2.16$	$24.41\pm 1.92\;(n=50)$	$20.24\pm 3.56\;(n=25)$
$\{0.8,0.4,0.2\}$	$20.92\pm 2.37$	$26.21\pm 2.16$	$21.12\pm 3.49$
$\{0.9,0.6,0.3,0.1\}$	$21.27\pm 2.38$	$26.78\pm 2.15$	$21.43\pm 3.48$
$\{0.8,0.4,0.2,0.1\}$	$21.34\pm 2.39$	$26.89\pm 2.15$	$21.52\pm 3.51$

Appendix

Table 7: Effect of the re-noising schedule

\sigma_{m}

. We vary the re-noising schedule across refinement iterations while keeping all other components fixed. Results report PSNR (dB) over the corrupted support as mean

\pm

standard deviation. Unless otherwise indicated, results are evaluated over 100 images. The highest mean in each column is shown in bold .

Figure 4: Qualitative effect of corruption-mask errors. We compare $\mathrm{SORD}{}$ using the exact corruption support or with dilated, eroded, or shifted masks. Overestimating the support causes the clean prior to regenerate some originally uncorrupted pixels, whereas underestimating the support leaves portions of the corruption outside $\Omega$ , where they are treated as trusted observations and therefore are not corrected.

Method	MNIST No mask	MNIST Exact	Natural No mask	Natural Exact	CIFAR-10 No mask	CIFAR-10 Exact
Input $y$	$12.09$ $\pm\,2.49$	$12.09$ $\pm\,2.49$	$9.37$ $\pm\,1.63$	$9.37$ $\pm\,1.63$	$7.92$ $\pm\,1.91$	$7.92$ $\pm\,1.91$
$\mathrm{SORD}{}$	$20.29$ $\pm\,3.38$	$27.16$ $\pm\,2.05$	$16.42$ $\pm\,2.69$	$21.96$ $\pm\,2.33$	$\mathbf{16.00}$ $\pm\,3.38$	$22.05$ $\pm\,3.45$
$\mathrm{SORD}{}$ + matched contaminant DM	$18.44$ $\pm\,3.68$	$\mathbf{29.12}$ $\pm\,2.26$	$15.54$ $\pm\,2.51$	$\mathbf{22.98}$ $\pm\,2.15$	$14.91$ $\pm\,3.23$	$\mathbf{22.08}$ $\pm\,3.49$
SGM / PiGDM, one prior	$11.42$ $\pm\,3.11$	$15.60$ $\pm\,2.75$	$13.18$ $\pm\,2.04$	$14.77$ $\pm\,2.45$	$12.33$ $\pm\,2.95$	$13.98$ $\pm\,3.29$
SGM / PiGDM, two priors	$\mathbf{25.64}$ $\pm\,3.42$	$22.38$ $\pm\,3.89$	$\mathbf{18.90}$ $\pm\,2.11$	$19.42$ $\pm\,3.32$	$14.66$ $\pm\,2.83$	$15.25$ $\pm\,2.77$

Appendix

Table 8: Effect of support information and contaminant modeling. We ablate the use of the exact corruption support and an additional contaminant diffusion model on the three localized CelebA benchmarks. Results report regional PSNR (dB) over

\Omega

as mean

\pm

standard deviation over

100

images. “No mask” treats the full image as the possible corruption support, whereas “Exact” uses the ground-truth support. SGM uses the joint

\Pi

GDM sampler of Stevens et al. (2025) . The best mean in each column is shown in bold .

Piano target
Audio Interferer	Mix	$\boldsymbol{N}$	DPS Inpaint	DPS $\boldsymbol{\mu=\mu_{n}}$	DPS $\boldsymbol{\mu=0}$	MSDM	$\mathrm{SORD}$
IV instrument	SIR $0$	$60$	$-0.34$ $\pm\,6.17$	$-0.01$ $\pm\,0.05$	$-0.06$ $\pm\,0.43$	$\mathbf{5.32}$ $\pm\,7.64$	$1.12$ $\pm\,5.11$
IV instrument	SIR $5$	$60$	$-0.12$ $\pm\,5.67$	$0.00$ $\pm\,0.07$	$0.01$ $\pm\,0.09$	$1.40$ $\pm\,6.85$	$\mathbf{2.74}$ $\pm\,6.23$
IV instrument	$g=1$	$60$	$0.34$ $\pm\,0.92$	$-0.02$ $\pm\,0.13$	$-0.02$ $\pm\,0.12$	$\mathbf{6.48}$ $\pm\,9.06$	$1.29$ $\pm\,2.58$
Speech (IV)	SIR $0$	$160$	$1.02$ $\pm\,1.18$	$-0.01$ $\pm\,0.10$	$0.00$ $\pm\,0.05$	$\mathbf{8.25}$ $\pm\,8.64$	$5.51$ $\pm\,3.37$
Speech (IV)	SIR $5$	$160$	$1.85$ $\pm\,2.02$	$-0.03$ $\pm\,0.28$	$0.00$ $\pm\,0.05$	$2.00$ $\pm\,10.03$	$\mathbf{6.40}$ $\pm\,3.39$

Appendix

Table 9: Localized structured corruption removal across image and audio domains. Audio results report windowed SI-SDR improvement (SI-SDRi, dB) for piano, guitar, bass, and drums targets under localized instrumental and speech interference. All values are mean

\pm

standard deviation. IV and OOV denote MSDM in-vocabulary and out-of-vocabulary interferers, respectively; for speech, IV uses MSDM augmented with a speech prior, while OOV uses the original four-source MSDM without a speech prior. The setting

g=1

denotes the unnormalized mixture. SGM and MSDM use explicit contaminant/source priors, whereas

\mathrm{SORD}{}

uses only the clean target prior. The highest mean in each row is shown in bold .

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