Summary of Taming Score-based Diffusion Priors For Infinite-dimensional Nonlinear Inverse Problems, by Lorenzo Baldassari et al.
Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problems
by Lorenzo Baldassari, Ali Siahkoohi, Josselin Garnier, Knut Solna, Maarten V. de Hoop
First submitted to arxiv on: 24 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Numerical Analysis (math.NA)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This research introduces a novel sampling method for solving Bayesian inverse problems in function space without assuming log-concavity of the likelihood. The approach utilizes infinite-dimensional score-based diffusion models as a prior, enabling posterior sampling through Langevin-type MCMC algorithms on function spaces. A convergence analysis is conducted, building upon traditional regularization-by-denoising methods and weighted annealing. The obtained bound explicitly depends on the approximation error of the score, highlighting the importance of accurate score approximations for well-calibrated posteriors. The method’s potential is demonstrated through stylized and PDE-based examples, showcasing the validity of the convergence analysis. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research introduces a new way to solve complex problems by combining different mathematical techniques. It shows how to use this approach to solve Bayesian inverse problems in function space without making certain assumptions. The method uses infinite-dimensional score-based diffusion models as a prior and then applies a specific type of Markov chain Monte Carlo algorithm to sample from the posterior distribution. The researchers also provide a detailed analysis of when and why their method works, including some examples that demonstrate its power. |
Keywords
» Artificial intelligence » Diffusion » Likelihood » Regularization
