Reconstructing Multi-Scale Physical Fields from Extremely Sparse Measurements with an Autoencoder-Diffusion Cascade

arXiv:2512.01572v3 Announce Type: replace-cross Abstract: Extreme sensor sparsity makes full-field reconstruction a fundamentally ill-posed problem in scientific sensing,where the goal is to infer physical fields from sparse measurements.In this regime,the posterior is severely underconstrained and inherently multimodal,making its approximation highly ill-conditioned.Specifically,deterministic mappings collapse uncertainty,direct conditional learning cannot cover the space of possible observatio