My research develops computational and learning-based methods for Bayesian inference from partial and noisy observations, with Bayesian inverse problems and data assimilation as two central settings. I am particularly interested in representing, learning, and sampling complex posterior distributions in high-dimensional systems. My current work combines conditional generative modeling and measure transport for posterior sampling, machine-learning-enhanced ensemble methods for nonlinear and non-Gaussian filtering, and transformers and attention as operators on probability measures. This measure-theoretic perspective connects practical algorithms with theoretical questions about continuum limits, permutation invariance, and generalization across ensemble sizes. During my Ph.D., I developed graph-based semi-supervised and active-learning methods for imaging and inverse problems. These methods use data geometry as a structural regularizer and adaptively select informative labels, providing a foundation for my broader interest in inference from limited observations.