# Self-diffusion for Solving Inverse Problems

arXiv: https://arxiv.org/abs/2510.21417 · HTML: https://mlsanity.com/paper/2510.21417/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 33 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Raw High-Definition Radar for Multi-Task Learning](https://mlsanity.com/paper/2112.10646/) (2021)
- [Compressed Sensing with Deep Image Prior and Learned Regularization](https://mlsanity.com/paper/1806.06438/) (2018)
- [Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models](https://mlsanity.com/paper/2202.01479/) (2022)
- [Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators](https://mlsanity.com/paper/1910.14634/) (2019)
- [Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation](https://mlsanity.com/paper/2005.03991/) (2020)
- [IMJENSE: Scan-specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI](https://mlsanity.com/paper/2311.12892/) (2023)
- [Unsupervised Radar Point Cloud Enhancement via Arbitrary LiDAR Guided Diffusion Prior](https://mlsanity.com/paper/2505.09887/) (2025)

## Built on by (most cited first, 4 of 4)

- [Self-Diffusion Driven Blind Imaging](https://mlsanity.com/paper/2510.27439/) (2025)
- [Self-Flow-Matching assisted Full Waveform Inversion](https://mlsanity.com/paper/2603.13425/) (2026)
- [Trajectory Constraints for Imaging Inverse Problems](https://mlsanity.com/paper/2605.29012/) (2026)
- [Image Reconstruction from Phase with Untrained Neural Priors](https://mlsanity.com/paper/2609.30659/) (2026)

## Abstract (arXiv)

We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward noising process. This model is then used to sample clean solutions -- corresponding to posterior sampling from a Bayesian perspective -- that are consistent with the observed data under a specific task. In contrast, self-diffusion introduces a self-contained iterative process that alternates between noising and denoising steps to progressively refine its estimate of the solution. At each step of self-diffusion, noise is added to the current estimate, and a self-denoiser, which is a single untrained convolutional network randomly initialized from scratch, is continuously trained for certain iterations via a data fidelity loss to predict the solution from the noisy estimate. Essentially, self-diffusion exploits the spectral bias of neural networks and modulates it through a scheduled noise process. Without relying on pretrained score functions or external denoisers, this approach still remains adaptive to arbitrary forward operators and noisy observations, making it highly flexible and broadly applicable. We demonstrate the effectiveness of our approach on a variety of linear inverse problems, showing that self-diffusion achieves competitive or superior performance compared to other methods.