Diffusion models learn a prior distribution by learning to reverse a gradual noising process. As priors for inverse problems they are combined with the data term during sampling.
Reading order.
- The model: Diffusion Models, DDPM Forward Process, Noise Schedule, DDPM Ancestral Sampling, Sinusoidal Time Embedding.
- The continuous view: Continuous Limit of the DDPM Chain, Variance-Preserving SDE, Reverse-Time SDE, Probability Flow ODE, Euler-Maruyama Method.
- Scores: Score Function, Denoising Score Matching, Tweedie’s Formula.
- Inverse problems: Diffusion Posterior Sampling, DiffPIR, RED-Diff, Diffusion Proximal Operator, and Diffusion Models for EIT.
- Beyond pixels: Diffusion Models on Finite Element Spaces.
Related. Other learned priors: Learned Priors; the broader picture: Classical and Learned Priors.
References
- J. Ho, A. Jain, P. Abbeel (2020). Denoising Diffusion Probabilistic Models. NeurIPS 2020. 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
- H. Chung, J. Kim, M. T. McCann, M. L. Klasky, J. C. Ye (2023). Diffusion Posterior Sampling for General Noisy Inverse Problems. ICLR 2023. arXiv:2209.14687