Inverse Problem

Inverse problems aim to determine underlying causes from observed effects, a challenge prevalent across diverse scientific fields. Current research heavily focuses on leveraging pre-trained generative models, particularly diffusion models, as powerful priors within Bayesian inference frameworks, often incorporating techniques like projected gradient descent or Markov Chain Monte Carlo methods to improve sampling efficiency and robustness. These advancements are significantly impacting various applications, from image restoration and medical imaging to fluid dynamics and material science, by enabling more accurate and efficient solutions to complex inverse problems. The development of theoretically grounded methods, such as those based on invertible neural networks or regularization techniques, is also a key area of ongoing investigation to enhance both performance and reliability.