Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Data
arXiv:2601.18728v2 Announce Type: replace Abstract: Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or linearly corrupted measurements can be observed. Moreover, latent structures, such as manifold geometries, present in the data are important to extract for further downstream scientific analysis. In this work, we introduce Riemannian AmbientFlow, a framework for simultaneously learning a probabilistic generative
The paper represents a significant step forward in generative AI research, specifically addressing the challenge of learning from corrupted data and extracting latent manifold structures, which is a persistent problem in real-world applications.
This research could dramatically improve the utility of generative AI in fields where clean data is rare, such as scientific imaging and medical diagnostics, moving AI capabilities closer to robust real-world deployment.
Current generative models primarily rely on clean data, limiting their applicability; this work proposes a framework to overcome data corruption, expanding the scope and reliability of AI in noisy environments.
- · AI researchers
- · Medical imaging sector
- · Scientific research institutions
- · Generative AI developers
- · Sectors reliant solely on clean data approaches
- · Traditional data cleaning services
Improved generative models capable of robust learning from imperfect data.
Accelerated development of AI applications in fields with inherently noisy or incomplete datasets.
Enhanced scientific discovery and medical breakthroughs as AI can better interpret complex, real-world observations.
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Read at arXiv cs.LG