Livin' on a Prior: Likelihood Score Approximation for Inverse Problems

2026-09-28

AI Summary

This work addresses the challenges of handling heterogeneous degradation models and the scarcity of paired data in inverse problems by proposing the Likelihood Score Approximation (LSA) framework. LSA decouples the prior from the observation-conditioned model by freezing a pretrained generative prior and learning only the likelihood score from minimal paired samples. It supports diverse sampling paradigms, including diffusion and flow matching, while enabling flexible post-training substitution of priors and compatibility with various parameterized coordinate systems. Experiments demonstrate that LSA achieves state-of-the-art performance on image and speech inverse tasks using merely one ten-thousandth of the conventional training data, while substantially reducing computational overhead.

Abstract

Generative models have found great success as data-driven methods of solving inverse problems. Two popular approaches work either by combining a pretrained generative prior with a known degradation model, or by training a conditional generative model directly from paired data. We target a setting that spans both regimes: unknown degradations can be learned from few paired examples, while known degradations can be learned from self-generated samples. We introduce Likelihood Score Approximation (LSA), a generative framework that keeps a pretrained unconditional model fixed and learns an observation-conditioned model that approximates the likelihood score from paired samples. Within a conditional stochastic-interpolant framework, LSA can be trained in either score or velocity coordinates, independently of the unconditional model's native parameterization, and supports both deterministic and stochastic sampling. We further show empirically that the prior model can be swapped post-training while keeping the same LSA model. Across speech and image inverse problems, LSA operates effectively even at roughly 0.01% of the full training dataset. On the ImageNet-256 benchmark it achieves competitive or better restoration quality than strong posterior-sampling baselines while requiring up to several orders of magnitude fewer network evaluations.

Problem

• Inverse Problems
• Generative Models
• Few-shot Learning
• Unknown Degradations
• Likelihood Score

Innovation

• Likelihood Score Approximation
• Inverse Problems
• Stochastic Interpolants
• Few-shot Learning
• Generative Prior