Data assimilation is the process of estimating the time-evolving state of a dynamical system by integrating model predictions and noisy observations. It is commonly formulated as Bayesian filtering, but classical filters often struggle with accuracy or computational feasibility in high dimensions. Recently, score-based generative models have emerged as a scalable approach for high-dimensional data assimilation, enabling accurate modeling and sampling of complex distributions. However, existing score-based filters often specify the forward process independently of the data assimilation. As a result, the measurement-update step depends on heuristic approximations of the likelihood score, which can accumulate errors and degrade performance over time. Here, we propose a measurement-aware score-based filter (MASF) that defines a measurement-aware forward process directly from the measurement equation. This construction makes the likelihood score analytically tractable: for linear measurements, we derive the exact likelihood score and combine it with a learned prior score to obtain the posterior score. Numerical experiments covering a range of settings, including high-dimensional datasets, demonstrate improved accuracy and stability over existing score-based filters.

Weusedtheentireimagesthatthe CUBdataset has (train, val, andtest). For example, onthe CUBdataset, theperformancegain (fork =5) is 0.249, 1.035, and 2.276for miniImageNet, tieredImageNet, and ImageNet, respectively.

V olume-wise labeling in 3D medical images is a time-consuming task that requires expertise. As a result, there is growing interest in using semi-supervised learning (SSL) techniques to train models with limited labeled data.

Neural image compression has made a great deal of progress. State-of-the-art models are based on variational autoencoders and are outperforming classical models.

SSL based on persistent homology (PH), a mathematical tool for modeling topological features of data that persist across multiple scales.

Based on our framework, we also present a hybrid of DRL and EMalgorithms thathasaguaranteed convergencerate.

Such a problem seriously hinders the realistic landing of classical SSL.