# Robust and interpretable blind image denoising via bias-free convolutional neural networks

arXiv: https://arxiv.org/abs/1906.05478 · HTML: https://mlsanity.com/paper/1906.05478/

## Key facts

- Cited by 90 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2019.

## Built on by (most cited first, 30 of 90)

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- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
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- [B-cos Alignment for Inherently Interpretable CNNs and Vision Transformers](https://mlsanity.com/paper/2306.10898/) (2023)
- [Approaching Deep Learning through the Spectral Dynamics of Weights](https://mlsanity.com/paper/2408.11804/) (2024)
- [Transfer CLIP for Generalizable Image Denoising](https://mlsanity.com/paper/2403.15132/) (2024)
- [On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion models](https://mlsanity.com/paper/2402.03845/) (2024)
- [Learning multi-scale local conditional probability models of images](https://mlsanity.com/paper/2303.02984/) (2023)
- [Learn from Unpaired Data for Image Restoration: A Variational Bayes Approach](https://mlsanity.com/paper/2204.10090/) (2022)
- [A Rainbow in Deep Network Black Boxes](https://mlsanity.com/paper/2305.18512/) (2023)
- [Learning normalized image densities via dual score matching](https://mlsanity.com/paper/2506.05310/) (2025)
- [Learning Distortion Invariant Representation for Image Restoration from A Causality Perspective](https://mlsanity.com/paper/2303.06859/) (2023)
- [Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problems](https://mlsanity.com/paper/2310.11838/) (2023)
- [Adaptive Denoising via GainTuning](https://mlsanity.com/paper/2107.12815/) (2021)
- [Stable and Interpretable Unrolled Dictionary Learning](https://mlsanity.com/paper/2106.00058/) (2021)
- [Score Priors Guided Deep Variational Inference for Unsupervised Real-World Single Image Denoising](https://mlsanity.com/paper/2308.04682/) (2023)
- [Scaling Laws For Deep Learning Based Image Reconstruction](https://mlsanity.com/paper/2209.13435/) (2022)
- [IDF: Iterative Dynamic Filtering Networks for Generalizable Image Denoising](https://mlsanity.com/paper/2508.19649/) (2025)
- [Normalization-Equivariant Neural Networks with Application to Image Denoising](https://mlsanity.com/paper/2306.05037/) (2023)
- [On the Asymptotic Mean Square Error Optimality of Diffusion Models](https://mlsanity.com/paper/2403.02957/) (2024)
- [Score-based generative models learn manifold-like structures with constrained mixing](https://mlsanity.com/paper/2311.09952/) (2023)
- [Blind denoising diffusion models and the blessings of dimensionality](https://mlsanity.com/paper/2602.09639/) (2026)
- [Measuring Perceptual Color Differences of Smartphone Photographs](https://mlsanity.com/paper/2205.13489/) (2022)
- [Benchmarking the Attribution Quality of Vision Models](https://mlsanity.com/paper/2407.11910/) (2024)
- [PnP-ReG: Learned Regularizing Gradient for Plug-and-Play Gradient Descent](https://mlsanity.com/paper/2204.13940/) (2022)
- [Perceptually Optimized Deep High-Dynamic-Range Image Tone Mapping](https://mlsanity.com/paper/2109.00180/) (2021)
- [Denoising Deep Generative Models](https://mlsanity.com/paper/2212.01265/) (2022)
- [What's Inside Your Diffusion Model? A Score-Based Riemannian Metric to Explore the Data Manifold](https://mlsanity.com/paper/2505.11128/) (2025)

## Abstract (arXiv)

Deep convolutional networks often append additive constant ("bias") terms to their convolution operations, enabling a richer repertoire of functional mappings. Biases are also used to facilitate training, by subtracting mean response over batches of training images (a component of "batch normalization"). Recent state-of-the-art blind denoising methods (e.g., DnCNN) seem to require these terms for their success. Here, however, we show that these networks systematically overfit the noise levels for which they are trained: when deployed at noise levels outside the training range, performance degrades dramatically. In contrast, a bias-free architecture -- obtained by removing the constant terms in every layer of the network, including those used for batch normalization-- generalizes robustly across noise levels, while preserving state-of-the-art performance within the training range. Locally, the bias-free network acts linearly on the noisy image, enabling direct analysis of network behavior via standard linear-algebraic tools. These analyses provide interpretations of network functionality in terms of nonlinear adaptive filtering, and projection onto a union of low-dimensional subspaces, connecting the learning-based method to more traditional denoising methodology.