[2512.17051] SFBD-OMNI: Bridge models for lossy measurement restoration with limited clean samples

Computer Science > Machine Learning arXiv:2512.17051 (cs) [Submitted on 18 Dec 2025 (v1), last revised 6 Apr 2026 (this version, v2)] Title:SFBD-OMNI: Bridge models for lossy measurement restoration with limited clean samples Authors:Haoye Lu, Yaoliang Yu, Darren Lo View a PDF of the paper titled SFBD-OMNI: Bridge models for lossy measurement restoration with limited clean samples, by Haoye Lu and 2 other authors View PDF HTML (experimental) Abstract:In many real-world scenarios, obtaining fully observed samples is prohibitively expensive or even infeasible, while partial and noisy observations are comparatively easy to collect. In this work, we study distribution restoration with abundant noisy samples, assuming the corruption process is available as a black-box generator. We show that this task can be framed as a one-sided entropic optimal transport problem and solved via an EM-like algorithm. We further provide a test criterion to determine whether the true underlying distribution is recoverable under per-sample information loss, and show that in otherwise unrecoverable cases, a small number of clean samples can render the distribution largely recoverable. Building on these insights, we introduce SFBD-OMNI, a bridge model-based framework that maps corrupted sample distributions to the ground-truth distribution. Our method generalizes Stochastic Forward-Backward Deconvolution (SFBD; Lu et al., 2025) to handle arbitrary measurement models beyond Gaussian corruption. Exper...