We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime based on one-step generative transport. Building on the Mean Flows, we learn a fully conditional amortized sampler with a neural-operator backbone that maps a reference Gaussian noise to approximate posterior samples. We show that while white-noise references may be admissible at fixed discretization, they become incompatible with the function-space limit, leading to instability in inference for Bayesian problems arising from PDEs. To address this issue, we adopt a prior-aligned anisotropic Gaussian reference distribution and establish the Lipschitz regularity of the resulting transport. Our method is not distilled from MCMC: training relies only on prior samples and simulated partial and noisy observations. Once trained, it generates a $64\times64$ posterior sample in $\sim 10^{-3}$s, avoiding the repeated PDE solves of MCMC while matching key posterior summaries.

We consider a family of problems that are concerned about making predictions for the majority of unlabeled, graph-structured data samples based on a small proportion of labeled samples. Relational information among the data samples, often encoded in the graph/network structure, is shown to be helpful for these semi-supervisedlearningtasks.

This is the full version of the paper Scott Rettberg presented for me at ISEA 2004 in Helsinki, on August 20, 2004. I slightly abbreviated the text he read so it would fit in the alloted time. The text that I sumitted to ISEA was abbreviated further so as to not exceed the (believe it or not) 13250 character limit. As I started researching this topic, I gave a preliminary talk at the History of Material Texts workshop; that text is online. If you'd like to correspond about the topic and correct or inform me about the use of print-based interfaces, please contact me: nickm at this domain.