The recent advancements in the field of multi-target filtering and inverse problem solving have shown significant progress, particularly in the integration of continuous-time dynamics and discrete-time measurements. Innovations in Gaussian continuous-discrete multi-target filters have enabled more accurate tracking of target movements modeled by stochastic differential equations, enhancing the robustness and precision of multi-target filtering algorithms. In the realm of inverse problem solving, there has been a notable shift towards optimizing the integration of measurement information within diffusion models, leading to faster and more accurate solutions. Methods like Guided Decoupled Posterior Sampling and Measurements Optimization have demonstrated state-of-the-art performance by effectively leveraging data consistency constraints and optimizing measurement incorporation, respectively. These developments not only improve the efficiency of the inverse problem-solving process but also enhance the quality of the generated images. Additionally, novel particle-based sampling techniques, such as Path-Guided Particle-based Sampling, have shown promise in Bayesian inference tasks by efficiently guiding particles along optimized density paths, thereby improving inference accuracy and calibration. Overall, the field is moving towards more integrated and optimized approaches that combine theoretical advancements with practical efficiency, setting new benchmarks in both multi-target filtering and inverse problem solving.