The field of inverse problems and geometric solvers is witnessing significant advancements with the development of novel frameworks and algorithms. Researchers are exploring new approaches to solve inverse problems without relying on pre-trained generative models, and are introducing innovative methods to reason about geometric problems in pixel space. The use of diffusion models, operator-learning-driven data super-resolution, and black box variational inference schemes are some of the key areas of focus. These advancements have the potential to improve the accuracy and efficiency of inverse problem solving and geometric computations. Noteworthy papers in this area include: Self-diffusion for Solving Inverse Problems, which proposes a novel framework for solving inverse problems without pre-trained generative models. Visual Diffusion Models are Geometric Solvers, which demonstrates the effectiveness of visual diffusion models in solving geometric problems. Adaptive Stochastic Coefficients for Accelerating Diffusion Sampling, which introduces a novel single-step SDE solver for accelerating diffusion sampling. Transcending Sparse Measurement Limits: Operator-Learning-Driven Data Super-Resolution for Inverse Source Problem, which presents a modular framework for improving multi-source localization from extremely sparse single-frequency measurements.