Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse Problem

What the math gives to ML

The paper's transferable asset is a continuous normalizing flow defined directly on a separable Hilbert space, allowing a simple Gaussian measure over functions to be transported into a learned, informative function-space prior. This is more than an ordinary finite-dimensional CNF when the target object is a field, trajectory, or operator input: the representation can remain resolution-independent and can encode correlations across discretization levels. The most practical neural-network transfer is a spectrally truncated Hilbert-space CNF whose vector field is implemented by a neural operator or basis-space MLP, with likelihood correction computed from the Jacobian trace and tested for mesh-resolution invariance.