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Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration
Yunjin Chen, Thomas Pock
Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image restoration problems. By embodying recent improvements in nonlinear diffusion models, we propose a dynamic nonlinear reaction diffusion model with time-dependent parameters (\ie, linear filters and influence functions). In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are simultaneously learned from training data through a loss based approach. We call this approach TNRD -- \textit{Trainable Nonlinear Reaction Diffusion}. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for the tested applications. Our trained models preserve the structural simplicity of diffusion models and take only a small number of diffusion steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Color Image Denoising | Darmstadt Noise Dataset | TNRD | PSNR (sRGB) | 33.65 | #6 of 6 | Archive leaderboard | report |
| Color Image Denoising | Darmstadt Noise Dataset | TNRD | SSIM (sRGB) | 0.8306 | #6 of 6 | Archive leaderboard | report |
| Denoising | Darmstadt Noise Dataset | TNRD | PSNR | 33.65 | #8 of 10 | Archive leaderboard | report |
| Grayscale Image Denoising | BSD68 sigma15 | TNRD | PSNR | 31.42 | #13 of 16 | Archive leaderboard | report |
| Grayscale Image Denoising | BSD68 sigma25 | TNRD | PSNR | 28.92 | #15 of 16 | Archive leaderboard | report |
| Grayscale Image Denoising | Urban100 sigma15 | TNRD | PSNR | 31.98 | #7 of 7 | Archive leaderboard | report |
| Image Super-Resolution | Set14 - 4x upscaling | TNRD | PSNR | 27.68 | #87 of 104 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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