Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolants

TL;DR

This paper introduces a novel, efficient method called SCSI for generative modeling from corrupted data using self-consistent transport maps, applicable to inverse problems with black-box corruption channels.

Contribution

The paper proposes a self-consistent stochastic interpolant method that inverts corruption channels for generative modeling, with theoretical guarantees and practical efficiency.

Findings

Outperforms variational methods in efficiency and flexibility

Handles arbitrary nonlinear corruption models with black-box access

Demonstrates superior results in image processing and scientific reconstruction

Abstract

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. Our source code is publicly available at https://github.com/modichirag/SCSI