活在先验上：逆问题的似然分数近似

中文摘要 AI 辅助

生成模型作为数据驱动的逆问题求解方法已取得巨大成功。两种流行的方法要么将预训练的生成先验与已知的退化模型相结合，要么直接从成对数据训练条件生成模型。我们针对跨越这两种机制的场景：未知退化可以从少量成对示例中学习，而已知退化可以从自生成样本中学习。我们提出了似然分数近似（LSA），一种生成框架，它保持预训练的无条件模型固定，并学习一个观测条件模型，从成对样本中近似似然分数。在条件随机插值框架内，LSA可以在分数或速度坐标中训练，独立于无条件模型的原始参数化，并支持确定性和随机采样。我们进一步通过实验表明，先验模型可以在训练后交换，同时保持相同的LSA模型。在语音和图像逆问题中，LSA即使在完整训练数据集的大约0.01%的情况下也能有效运行。在ImageNet-256基准上，它实现了与强后验采样基线相当或更好的恢复质量，同时需要的网络评估次数少几个数量级。

英文摘要

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.

发表机构

• University of Hamburg（汉堡大学）

机构由 AI 辅助整理，请以论文原文为准。