Noise Flow: Noise Modeling with Conditional Normalizing Flows

—Supplemental Material—

Abdelrahman Abdelhamed1,2

1York University

Marcus A. Brubaker2

2Borealis AI

Michael S. Brown1,3

3Samsung AI Center, Toronto

{kamel,mbrown}@eecs.yorku.ca, marcus.brubaker@borealisai.com

In this supplemental document, we elaborate more on the

application of Noise Flow for training convolutional neural

network (CNN) image denoisers and present more gener-

ated noise samples from Noise Flow for visual inspection.

Denoising Training Loss

Figure 1 shows the training loss over 2000 epochs of

the DnCNN [1] image denoiser using the three noise syn-

thesis models: (1) DnCNN-Gauss: the Gaussian model;

(2) DnCNN-CamNLF: the heteroscedastic Gaussian model

represented by the camera-calibrated noise level functions

(NLFs); and (3) DnCNN-NoiseFlow: our Noise Flow

model. Despite that training loss of the DnCNN-CamNLF

is the lowest, the training behaviour indicated that DnCNN-

NoiseFlow is the most stable. The DnCNN-Gauss model

is also stable, however, it still yields lower testing perfor-

mance, as shown in Figure 2.

Denoising Testing Results

Figure 2 shows the testing peak signal-to-noise ratio

(PSNR) over 2000 epochs of the three models from Fig-

ure 1. DnCNN-CamNLF outperforms the DnCNN-Gauss

models by a small margin, despite the lower training loss

of the former. The DnCNN-NoiseFlow model yields the

best performance despite having slightly higher training

loss than DnCNN-CamNLF.

Figure 3 shows more denoising results from the three

models for visual inspection. The samples confirm the bet-

ter performance of the DnCNN-NoiseFlow model and the

importance of having more accurate noise models for gen-

erating realistic synthetic noise.

More Generated Noise Samples

Figure 4 shows more generated noise samples from the

Noise Flow model compared to the Gaussian and the cam-

era NLF models. Noise Flow samples are much closer to

the real samples in terms of the marginal KL divergence.

We show the corresponding ISO level and lighting condi-

tion on the left.

0 250 500 750 1000 1250 1500 1750 2000Epoch

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Trai

ning

loss

(L2)

DnCNN-GaussDnCNN-CamNLFDnCNN-NoiseFlow

Figure 1: Results of training the DnCNN [1] image denoiser

with synthetic noise generated by: the Gaussian model; the

camera NLFs; and our Noise Flow model.

0 250 500 750 1000 1250 1500 1750 2000Epoch

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PSNR

DnCNN-GaussDnCNN-CamNLFDnCNN-NoiseFlow

Figure 2: Testing PSNR results corresponding to the three

model from Figure 1. The DnCNN model trained on noise

generated with Noise Flow yields the best PSNRs.

References

[1] K. Zhang, W. Zuo, Y. Chen, D. Meng, and L. Zhang. Beyond a

Gaussian denoiser: Residual learning of deep CNN for image

denoising. TIP, 2017. 1

1

a  Real Noisy  Gaussia  Ca era NLF d  Noise Flow e  Grou d Truth a  Real Noisy  Gaussia  Ca era NLF d  Noise Flow e  Grou d Truth

Figure 3: Sample denoising results from the DnCNN denoiser trained on three different noise synthesis methods:(b) Gaussian;

(c) camera NLF; and (d) Noise Flow. (a) Real noisy image. (e) Ground truth.

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a  Gaussia  Ca era NLF  Noise Flow d  Real Noise e  Cleaa  Gaussia  Ca era NLF  Noise Flow d  Real Noise e  Clea

Figure 4: More generated noise samples from (c) Noise Flow compared to samples from (a) the Gaussian and (b) camera

NLF models. (d) Real noise. (e) Clean image. Noise Flow samples are much closer to the real samples in terms of the

marginal KL divergence. We show the corresponding ISO level and lighting condition on the left.