Learning to Recorrupt: Noise Distribution Agnostic Self-Supervised Image Denoising

Brayan Monroy; Jorge Bacca; Julián Tachella

eess.IVMar 26, 2026

Learning to Recorrupt: Noise Distribution Agnostic Self-Supervised Image Denoising

Authors: Brayan Monroy, Jorge Bacca, Julián Tachella

Organizations: Universidad Industrial de Santander, Colombia · CNRS, ENS de Lyon, France

Abstract

Self-supervised image denoising methods have traditionally relied on architectural constraints, pseudo-pair constructions, or specialized loss functions to avoid the trivial identity mapping. Among these, approaches such as Noisier2Noise or R2R create training pairs by adding synthetic noise to noisy images. While effective, these recorruption-based approaches require precise knowledge of the noise distribution, which is often unavailable. We present Learning to Recorrupt (L2R), a self-supervised framework that does not require exact knowledge of the noise distribution. Our method introduces a learnable recorruptor jointly optimized with the denoiser through a min--max saddle-point objective. The proposed method achieves state-of-the-art performance among methods without prior knowledge of the noise distribution across unconventional and heavy-tailed noise distributions, such as log-gamma and Laplace, as well as spatially correlated noise, while obtaining competitive results on real-world denoising benchmarks characterized by signal-dependent noise.

Figures & tables

Figure 1: Non-Gaussian Image Denoising. L2R is capable of handling complex non-Gaussian noise models without requiring prior knowledge of the noise distribution statistics, including log-gamma, Laplace, and correlated noise.

Figure 2: Learning to Recorrupt. Given a noisy image $\boldsymbol{y}$ with unknown noise, L2R generates a recorrupted version $\boldsymbol{y}_{1}$ through a learned recorruptor $h$ to enable self-supervised denoiser training.

Method	$p_{\boldsymbol{\varepsilon}}$	Log-gamma Noise			Laplace Noise			Correlated Noise
Method	known?	$\ell$	BSDS500	DIV2K	$b$	BSDS500	DIV2K	$\sigma$	BSDS500	DIV2K
Supervised	no		31.44/0.898	31.96/0.894		29.48/0.856	30.21/0.859		30.56/0.897	30.75/0.887
GR2R	yes		31.14/0.889	31.98/0.893		28.10/0.803	28.74/0.807		30.43/0.893	30.61/0.884
SURE	yes		28.33/0.796	28.61/0.781		27.07/0.748	27.60/0.747		30.37/0.891	30.60/0.882
R2R	yes		28.63/0.809	29.03/0.799		27.85/0.797	28.52/0.804		24.52/0.653	24.97/0.634
UNSURE	no	1.0	27.83/0.756	28.11/0.737	0.1	22.93/0.615	23.42/0.639	0.2	29.56 / 0.841	29.56 / 0.821

Table 1: Non-Gaussian Denoising. Performance under different types of non-Gaussian noise. Best and second-best self-supervised results are shown in bold and underlined, respectively. Gray rows are reference methods excluded from the ranking.

Figure 3: Non-Gaussian Denoising. Visual comparison on representative BSDS500 crops corrupted by log-gamma, Laplace, and spatially correlated noise. Columns show the noisy input, SURE, UNSURE, R2R, NBR2NBR, and the proposed L2R, followed by the ground truth. Numbers in each panel report PSNR (dB) / SSIM.

Figure 4: Visualization of qualitative results on a sample image from the SIDD benchmark.

Methods	Blind-spot	Train Cost	SIDD Val	SIDD Bench
Supervised	no	$\times 1$	51.19/0.991	50.61/0.991
Noise2Noise	no	$\times 1$	51.21/0.991	50.62/0.991
Noisy-as-Clean (NAC)	no	$\times 1$	43.24/0.961	-
R2R	no	$\times 1$	47.20/0.980	46.70/0.978
Noise2Void (N2V)	yes	$\times 1$	48.55/0.984	48.01/0.983
NBR2NBR	no	$\times 2$	51.06/0.991	50.47/0.990

Table 2: Real-world denoising performance on SIDD. Training cost is reported relative to Supervised training. Best and second-best self-supervised results are highlighted.

Figure 5: Blind denoising results of Cryo-EM data using the L2R method and PG-UNSURE.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Overview of the four recorruptor parameterizations. (a) Additive i.i.d. noise; (b) additive noise with spatial correlations; (c) local recorruptor, with parameters shared across images and pixelwise scaling from

\boldsymbol{y}

; and (d) global recorruptor, which uses image-level information from

\boldsymbol{y}

to estimate image-specific noise statistics and monotonic-map parameters.

Method	$p_{\boldsymbol{\varepsilon}}$	Poisson–Gaussian Noise
Method	known?	$\gamma/\sigma$	BSDS500	DIV2K
Supervised	no		28.44/0.833	29.45/0.845
PG-SURE	yes		27.21/ 0.776	27.94/ 0.783
PG-UNSURE	no	0.05/	27.44 /0.774	28.14 /0.771
NBR2NBR	no	0.05	27.12/0.751	27.64/0.744
Blind2Sound	no		27.30/0.793	27.89/0.789

Appendix

Table 3: Denoising performance in removing Poisson–Gaussian noise.

Figure 7: Poisson–Gaussian Denoising. Visual comparison on representative BSDS500 crops corrupted by Poisson–Gaussian Noise. Columns show the noisy input, PG-SURE, PG-UNSURE, GR2R, NBR2NBR, and the proposed L2R, followed by the ground truth.

network setup $h(\cdot)$	PSNR	SSIM
Supervised	31.44	0.898
Oracle (GR2R)	31.14	0.889
No learning	20.00	0.415
MLP	30.45	0.860
MLP + Residual	30.36	0.858
MLP + Id-pretrain	30.42	0.856

Appendix

Table 4: Ablation of the design of model

h

Joint?	$f$ -loss (min)	$h$ -loss (max)	PSNR	SSIM
no	$\\|f(\boldsymbol{y}_{1})-\boldsymbol{y}_{2}\\|_{2}^{2}$	$h(\boldsymbol{w}^{\prime})^{\top}f(\boldsymbol{y}_{1})$	29.72	0.854
no	$\\|f(\boldsymbol{y}_{1})-\boldsymbol{y}_{2}\\|_{2}^{2}+\frac{1}{\tau}\cdot(\boldsymbol{y}_{2}+\boldsymbol{y})^{\top}h(\boldsymbol{w}^{\prime})$		29.74	0.854
no	$\\|f(\boldsymbol{y}_{1})-\boldsymbol{y}\\|_{2}^{2}\hskip 4.49997pt+2\cdot h(\boldsymbol{w}^{\prime})^{\top}f(\boldsymbol{y}_{1})$		29.38	0.841
no	$\\|f(\boldsymbol{y}_{1})-\boldsymbol{y}\\|_{2}^{2}\hskip 4.49997pt+\frac{2}{\tau}\cdot h(\boldsymbol{w}^{\prime})^{\top}f(\boldsymbol{y}_{1})$		29.83	0.859
yes	$\\|f(\boldsymbol{y}_{1})-\boldsymbol{y}\\|_{2}^{2}\hskip 4.49997pt+\frac{2}{\tau}\cdot h(\boldsymbol{w}^{\prime})^{\top}f(\boldsymbol{y}_{1})$		29.78	0.860
yes	$\\|f(\text{sg}[\boldsymbol{y}_{1}])-\boldsymbol{y}\\|_{2}^{2}+\frac{2}{\tau}\cdot h(\boldsymbol{w}^{\prime})^{\top}f(\text{sg}[\boldsymbol{y}_{1}])$		29.85	0.863

Appendix

Table 5: Ablation

f

-loss and

h

-loss. Correlated denoising performance for different types of

f

-loss and

h

-loss with

\sigma=0.2

\text{sg}[\cdot]

denotes the stop-gradient function.

Depth	# Neurons	PSNR	SSIM
2	16	$30.57$	$0.871$
2	8	$30.60$	$0.874$
3	8	$30.56$	$0.870$
4	8	$30.53$	$0.871$
2	4	$30.50$	$0.866$
3	4	$30.60$	$0.872$

Appendix

Table 6: Performance for different model sizes of

h

on log-gamma noise.

Noise Model	$k$ -size	$s(\boldsymbol{y})$	PSNR	SSIM
Log-gamma	$1\times 1$	no	$\boldsymbol{30.77}$	$\boldsymbol{0.871}$
$\ell=1.0$	$3\times 3$	no	$\underline{29.93}$	$\underline{0.837}$
	$1\times 1$	yes	$26.98$	$0.721$
	$3\times 3$	yes	$24.02$	$0.657$
Correlated	$1\times 1$	no	$24.21$	$0.660$
$\sigma=0.2$	$3\times 3$	no	$\boldsymbol{29.85}$	$\boldsymbol{0.863}$

Appendix

Table 7: Influence of the architecture design

h

. The table reports the ablation results for different kernel sizes and

s(\boldsymbol{y})

-scaling configurations, evaluated under three noise models: element-wise log-gamma noise, spatially correlated noise, and signal-dependent Poisson–Gaussian noise.

$\tau$	0.1	0.3	0.4	0.5	0.6	0.7	0.9
PSNR	28.83	30.21	29.95	30.34	29.78	29.59	29.26
SSIM	0.821	0.869	0.865	0.868	0.860	0.854	0.843

Appendix

Table 8: Sensitivity to

\tau

on log-gamma noise

\ell=1.0

Parameter	Values / PSNR (dB)	avg PSNR (mean $\pm$ std.)
Recorruption ( $\tau$ )	$\begin{array}[]{c\|c\|c\|c\|c}\small 0.6&\small 0.8&\mathbf{1.0}&\small 1.25&\small 1.67\\ \hline\cr\small 50.68&\small 51.04&\textbf{51.32}&\small 51.20&\small 50.98\end{array}$	$51.04\pm 0.24$
Learning Ratio ( $R_{lr}$ )	$\begin{array}[]{c\|c\|c\|c\|c}\small 0.1&\small 0.3&\mathbf{0.5}&\small 0.7&\small 0.9\\ \hline\cr\small 50.76&\small 51.09&\textbf{51.32}&51.14&51.30\end{array}$	$51.12\pm 0.22$
RNG Seed	$\begin{array}[]{c\|c\|c\|c\|c}\small 0&\small 1&2&\small 3&\small 4\\ \hline\cr 51.29&51.15&\textbf{51.32}&51.27&51.25\end{array}$	$51.25\pm 0.06$

Appendix

Table 9: Training stability on SIDD under variations of the main optimization parameters.

Figure 8: Learned maps and spatial kernel. From left to right , the panels show the learned recorruption maps for log-gamma and Laplace noise and the learned kernel for correlated noise.

Figure 9: Training dynamics of the implicit correlation terms. Top: noise correlation

\mathcal{C}_{\varepsilon}

( black ) and auxiliary correlation

\mathcal{C}_{h}

( blue ) versus epoch. Bottom: residual gap

\mathcal{C}_{\mathrm{\Delta}}

( green ). Both inner-product terms settle near zero. The residual gap decreases and stabilizes near zero, supporting the empirical alignment described in Eq. ( 21 ).

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