The field of diffusion models is rapidly advancing, with recent developments showing great promise in simulating complex dynamical systems and solving inverse problems. Researchers are exploring the connections between diffusion models and traditional methods, such as molecular dynamics and stochastic differential equations, to create more efficient and accurate simulations. The use of diffusion models in inverse problems is also gaining traction, with new methods being proposed to improve the accuracy and efficiency of solving these problems. Notably, the application of diffusion models to partially observable dynamical systems and the development of multiscale inference schemes are allowing for more accurate predictions and improved performance. Overall, the field is moving towards more innovative and effective applications of diffusion models. Noteworthy papers include:

• A paper that proves the equivalence between denoising diffusion samplers and Euler-Maruyama integrators for overdamped Langevin dynamics, allowing for the interpretation of diffusion models as molecular dynamics simulators.
• A paper that proposes a diffusion-based surrogate model for time-varying underwater acoustic channels, which can generate diverse and statistically realistic channel realizations.
• A paper that presents a multiscale inference scheme for diffusion models to predict partially observable dynamical systems, which can capture long-range temporal dependencies without increasing computational cost.
• A paper that introduces aRestart for Posterior Sampling framework for solving inverse problems using pre-trained diffusion models, which achieves faster convergence and superior reconstruction quality compared to existing diffusion-based baselines.