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

TL;DR

This paper introduces SFBD-OMNI, a framework that restores true data distributions from noisy, partial measurements using a bridge model and optimal transport, even with limited clean samples.

Contribution

It extends SFBD to handle arbitrary measurement models and proposes a new test criterion for distribution recoverability with limited clean data.

Findings

Significant improvements in distribution restoration across benchmarks.

The method effectively handles various measurement models beyond Gaussian.

A small number of clean samples can enable recovery in otherwise unrecoverable cases.

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. Experiments across benchmark datasets and diverse measurement settings demonstrate significant improvements in both qualitative and quantitative performance.