构建可逆生成模型，统一解决正向与反向问题的模拟与推断。
An invertible generative model for forward and inverse problems
- 用可逆流模型整合条件采样，实现正向模拟与反向推断。
- 通过变分方法直接从成对样本训练模型，无需显式似然函数。
- 适用于需双向生成的科学计算场景，如物理建模与图像重建。
我们将反问题置于贝叶斯框架下，旨在训练一个可逆生成模型，该模型既能进行模拟（即从似然采样），也能进行推断（即从后验采样）。我们称此类生成模型为可逆模拟器。首先，通过将上下三角归一化流与条件采样结合，构造出一个明确的可逆模拟器实例。接着，研究其基本结构特性，分析其非唯一性，并推导出一种变分公式，使生成模型能直接从成对样本中训练。最后，我们在解析可处理和简化的数值例子上验证了该框架，展示了其作为正向与反向问题条件生成建模的统一方法的潜力。
原文摘要 · Abstract (English)
We formulate inverse problems in a Bayesian framework and aim to train an invertible generative model that is capable of simulation (i.e., sampling from the likelihood) and inference (i.e., sampling from the posterior). We call such a generative model a Reversible Simulator. We first construct an explicit instance of a reversible simulator by combining lower and upper triangular normalizing flows associated with conditional sampling into a single invertible map. We then establish basic structural properties of this construction, investigate its non-uniqueness, and derive a variational formulation that enables the generative model to be trained directly from paired samples. Finally, we illustrate the proposed framework on analytically tractable and stylized numerical examples, demonstrating its potential as a unified approach to conditional generative modeling for forward and inverse problems.
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