Given an inverse problem with a normalizing flow prior, we wish to estimate the distribution of the underlying signal conditioned on the observations. We approach this problem as a task of conditional inference on the pre-trained unconditional flow model. We first establish that this is computationally hard for a large class of flow models. Motivated by this, we propose a framework for approximate inference that estimates the target conditional as a composition of two flow models. This formulation leads to a stable variational inference training procedure that avoids adversarial training. Our method is evaluated on a variety of inverse problems and is shown to produce high-quality samples with uncertainty quantification. We further demonstrate that our approach can be amortized for zero-shot inference.

翻译：鉴于先前流流正常化的反向问题,我们希望估计以观察为条件的基本信号的分布情况。我们将此问题作为预先训练的无条件流模式的有条件推断任务来对待。我们首先确定,对于一大批流模式来说,这是难以计算的结果。我们为此提出一个大致推论框架,用以估计两个流模式构成的有条件目标。这一提法导致一个稳定的可变推论培训程序,避免对抗性培训。我们的方法是针对各种反向问题进行评估的,并证明可以产生具有不确定性的高质量样本。我们进一步证明,我们的方法可以被零发推论分解。