Self-diffusion for Solving Inverse Problems
Guanxiong Luo, Shoujin Huang
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 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 on a clean dataset, 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.