# The Spectral Bias of the Deep Image Prior

arXiv: https://arxiv.org/abs/1912.08905 · HTML: https://mlsanity.com/paper/1912.08905/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2019.

## Built on by (most cited first, 21 of 21)

- [Overview frequency principle/spectral bias in deep learning](https://mlsanity.com/paper/2201.07395/) (2022)
- [DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2405.16749/) (2024)
- [Learning by Reconstruction Produces Uninformative Features For Perception](https://mlsanity.com/paper/2402.11337/) (2024)
- [On Measuring and Controlling the Spectral Bias of the Deep Image Prior](https://mlsanity.com/paper/2107.01125/) (2021)
- [Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems](https://mlsanity.com/paper/2503.13695/) (2025)
- [An Analytical Theory of Spectral Bias in the Learning Dynamics of Diffusion Models](https://mlsanity.com/paper/2503.03206/) (2025)
- [Zero-shot Blind Image Denoising via Implicit Neural Representations](https://mlsanity.com/paper/2204.02405/) (2022)
- [The Devil is in the Upsampling: Architectural Decisions Made Simpler for Denoising with Deep Image Prior](https://mlsanity.com/paper/2304.11409/) (2023)
- [Subspace Decomposition based DNN algorithm for elliptic type multi-scale PDEs](https://mlsanity.com/paper/2112.06660/) (2021)
- [Posterior temperature optimized Bayesian models for inverse problems in medical imaging](https://mlsanity.com/paper/2202.00986/) (2022)
- [PIP: Positional-encoding Image Prior](https://mlsanity.com/paper/2211.14298/) (2022)
- [Towards Architecture-Agnostic Untrained Network Priors for Image Reconstruction with Frequency Regularization](https://mlsanity.com/paper/2312.09988/) (2023)
- [HOIN: High-Order Implicit Neural Representations](https://mlsanity.com/paper/2404.14674/) (2024)
- [Optimal Eye Surgeon: Finding Image Priors through Sparse Generators at Initialization](https://mlsanity.com/paper/2406.05288/) (2024)
- [An unsupervised method for MRI recovery: Deep image prior with structured sparsity](https://mlsanity.com/paper/2501.01482/) (2025)
- [Image Reconstruction via Deep Image Prior Subspaces](https://mlsanity.com/paper/2302.10279/) (2023)
- [Conditioning Generative Latent Optimization for Sparse-View CT Image Reconstruction](https://mlsanity.com/paper/2307.16670/) (2023)
- [Neural Gradient Regularizer](https://mlsanity.com/paper/2308.16612/) (2023)
- [Automating Parameter Selection in Deep Image Prior for Fluorescence Microscopy Image Denoising via Similarity-Based Parameter Transfer](https://mlsanity.com/paper/2601.12055/) (2026)
- [Pooling-Based Context Modeling for Convolution-Free Deep Image Prior](https://mlsanity.com/paper/2607.02952/) (2026)
- [Spectral Considerations on Unsupervised Time-domain EEG Representation Learning with Deep Networks](https://mlsanity.com/paper/2610.16264/) (2026)

## Abstract (arXiv)

The "deep image prior" proposed by Ulyanov et al. is an intriguing property of neural nets: a convolutional encoder-decoder network can be used as a prior for natural images. The network architecture implicitly introduces a bias; If we train the model to map white noise to a corrupted image, this bias guides the model to fit the true image before fitting the corrupted regions. This paper explores why the deep image prior helps in denoising natural images. We present a novel method to analyze trajectories generated by the deep image prior optimization and demonstrate: (i) convolution layers of the an encoder-decoder decouple the frequency components of the image, learning each at different rates (ii) the model fits lower frequencies first, making early stopping behave as a low pass filter. The experiments study an extension of Cheng et al which showed that at initialization, the deep image prior is equivalent to a stationary Gaussian process.