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

2025-12-11

AI Summary

In scientific and engineering applications, clean ground-truth data are often unavailable; only noisy observations—degraded through unknown forward channels—are accessible. This poses a fundamental challenge for distribution-level inverse problem solving without paired training data or explicit knowledge of the degradation process. Method: We propose the Self-Consistent Stochastic Interpolator (SCSI), the first method enabling distribution-level inversion solely from a black-box forward model. SCSI constructs a stochastic interpolation framework grounded in optimal transport maps and alternates between self-consistent iterative optimization and denoising score estimation—bypassing explicit inverse modeling or variational lower bounds. Contribution/Results: We provide rigorous theoretical guarantees on convergence. Empirically, SCSI significantly outperforms state-of-the-art variational methods on natural image restoration and scientific reconstruction tasks. It achieves high computational efficiency, robust adaptability to strong nonlinear degradations, and principled theoretical foundations—establishing a new paradigm for generative modeling under unpaired, unknown degradation.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• Develops generative models from noisy, corrupted data without clean datasets.
• Inverts arbitrary nonlinear corruption channels using only black-box access.
• Provides efficient, flexible method for scientific and image inverse problems.

Innovation

• Iterative transport map updates using corrupted data
• Black-box access to corruption channel for inversion
• Self-consistent stochastic interpolants enable clean data generation