Diffusion models learn a data distribution by learning to reverse a process that gradually turns data into Gaussian noise.
- Forward (noising) process. Corrupt data with increasing amounts of Gaussian noise until only noise remains (see DDPM Forward Process, Noise Schedule and Variance-Preserving SDE).
- Learning. Train a network to predict the added noise, or equivalently the Score Function of the noisy marginals, at every noise level (see Denoising Score Matching).
- Generation. Start from pure noise and integrate the Reverse-Time SDE or the Probability Flow ODE with the learned score (see Euler-Maruyama Method and DDPM Ancestral Sampling).
As priors for inverse problems. A trained diffusion model is an operator-agnostic prior (see Learned Regularization). It is combined with the EIT forward model in three main ways:
- guidance of the reverse process with data gradients (Diffusion Posterior Sampling);
- alternating denoising and data-consistency prox steps (DiffPIR);
- a variational regulariser, independent of the sampling schedule (RED-Diff and Diffusion Proximal Operator).
All three rely on Tweedie’s Formula to estimate the clean image from a noisy one. For EIT-specific work see Diffusion Models for EIT.
References
- J. Sohl-Dickstein, E. Weiss, N. Maheswaranathan, S. Ganguli (2015). Deep Unsupervised Learning using Nonequilibrium Thermodynamics. ICML 2015. arXiv:1503.03585
- J. Ho, A. Jain, P. Abbeel (2020). Denoising Diffusion Probabilistic Models. NeurIPS 33. arXiv:2006.11239
- Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, B. Poole (2021). Score-Based Generative Modeling through Stochastic Differential Equations. ICLR 2021. arXiv:2011.13456