We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional inverse problems without the need for posterior training samples. We implement the method on multi-modal benchmark tasks in 2D and 3D to check for the efficacy. A critical observation of our study is the impact of the topology of the base distributions on the modelled posteriors. We find that standard unimodal base distributions fail to capture disconnected support, resulting in spurious probability bridges between modes. We demonstrate that initializing the flow with a Gaussian Mixture Model that matches the cardinality of the target modes significantly improves reconstruction fidelity, as measured by some distance and divergence metrics.

翻译：我们提出了一种利用似然加权重要性采样训练的归一化流进行摊销式后验估计的新方法。该技术能够在无需后验训练样本的情况下，高效推断高维逆问题中的理论参数。我们在二维和三维多模态基准任务上验证了该方法的有效性。本研究的一个关键发现是基础分布拓扑结构对建模后验的影响。我们发现标准的单峰基础分布无法捕捉非连通支撑集，导致模态间出现虚假概率桥接。通过使用与目标模态基数匹配的高斯混合模型初始化流，我们证明该方法能显著提升重构保真度，这一结论通过若干距离与散度度量指标得到验证。