CIF: Small: Flow Matching with Transport Identifiability

This project studies two important capabilities of modern artificial intelligence (AI). The first is translating information across different forms of data, such as converting text descriptions into images. The second is generating new content, such as creating realistic images, text or other data with desired characteristics. Recent advances in AI increasingly rely on learning smooth transformation processes between different forms of information, an emerging approach known as flow matching. Flow matching has demonstrated remarkable capabilities in data generation and transformation across a wide range of applications. However, it remains difficult to guarantee that these systems preserve the intended information during translation or maintain desired characteristics during content generation. These challenges become especially pronounced when the systems are trained using data from multiple domains that are not directly aligned. Establishing such guarantees is important for developing trustworthy and interpretable AI systems that are less susceptible to hallucinations and unintended distortions in scientific discovery, healthcare, and other data-intensive fields. The project will also support education and workforce development by engaging undergraduate, graduate, and K-12 students in research at the intersection of mathematics, data science, and machine learning. This project develops new mathematical foundations and computational methods for identifiable multi-domain data translation and generation using flow matching. The focus is on settings where data from multiple domains are not aligned or paired. Establishing identifiability (i.e., uniqueness of the learned translation and generation mechanisms) is particularly important because alternative solutions that may arise from non-uniqueness may fail to preserve intended content during translation or desired characteristics during generation. Unlike traditional approaches that explicitly represent transformation mappings, flow matching represents transformations through learned velocity fields, creating fundamentally new challenges for establishing identifiability. The first research thrust develops analytical and computational tools for multi-domain translation that preserve intended content across domains. The second thrust establishes theoretical and algorithmic foundations for controllable multi-domain generation, enabling desired characteristics to be reliably preserved. Across both thrusts, the research activities will develop principled learning objectives and transformation trajectories for flow matching, establish conditions under which desired translation and generation mechanisms can be uniquely identified, and design efficient learning algorithms with theoretical guarantees. The resulting methods will be evaluated over a variety of applications. By combining identifiability guarantees with the flexibility of flow matching, the developed methods are expected to enable semantic-preserving translation and content- or style-controlled generation under limited supervision, advancing the frontier of unsupervised cross-domain learning with flow matching. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.