Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolants
This addresses the challenge of generative modeling in scientific and engineering domains where only noisy, corrupted data are available, offering a flexible and efficient solution for inverse problems.
The paper tackles the problem of building generative models from corrupted data by introducing the self-consistent stochastic interpolant (SCSI) method, which iteratively updates a transport map to invert the corruption channel, demonstrating superior performance on inverse problems in image processing and scientific reconstruction with theoretical guarantees.
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.