Transport-based methods have emerged as a leading paradigm for building generative models from large, clean datasets. However, in many scientific and engineering domains, clean data are often unavailable: instead, we only observe measurements corrupted through a noisy, ill-conditioned channel. A generative model for the original data thus requires solving an inverse problem at the level of distributions. In this work, we introduce a novel approach to this task based on Stochastic Interpolants: we iteratively update a transport map between corrupted and clean data samples using only access to the corrupted dataset as well as black box access to the corruption channel. Under appropriate conditions, this iterative procedure converges towards a self-consistent transport map that effectively inverts the corruption channel, thus enabling a generative model for the clean data. We refer to the resulting method as the self-consistent stochastic interpolant (SCSI). It (i) is computationally efficient compared to variational alternatives, (ii) highly flexible, handling arbitrary nonlinear forward models with only black-box access, and (iii) enjoys theoretical guarantees. We demonstrate superior performance on inverse problems in natural image processing and scientific reconstruction, and establish convergence guarantees of the scheme under appropriate assumptions.

翻译：基于传输的方法已成为从大规模干净数据集构建生成模型的主流范式。然而，在许多科学与工程领域中，干净数据往往难以获取：我们仅能观测到通过噪声、病态通道退化的测量结果。因此，为原始数据构建生成模型需要在分布层面解决逆问题。本研究提出一种基于随机插值的新方法：我们仅利用退化数据集及对退化通道的黑盒访问权限，迭代更新退化数据与干净数据样本间的传输映射。在适当条件下，该迭代过程收敛于一个自洽的传输映射，可有效逆转退化通道，从而实现对干净数据的生成建模。我们将此方法称为自洽随机插值（SCSI）。该方法具有以下特点：（i）与变分替代方案相比计算效率更高；（ii）灵活性极强，仅需黑盒访问即可处理任意非线性前向模型；（iii）具备理论保证。我们在自然图像处理与科学重建的逆问题上展示了其优越性能，并在适当假设下证明了该方案的收敛性。