arXiv:2606.19894v1 Announce Type: new Abstract: The remarkable success of score-based diffusion models has spurred significant efforts to establish their theoretical foundations. However, existing complexity bounds for score approximation rely heavily on restrictive assumptions like Lipschitz continuous densities or smooth manifold supports, which are routinely violated by the singularities, sharp boundaries, and disjoint clusters inherent to real-world perceptual data. This work establishes a universal score approximation theorem that works for any distribution supported on any compact set of
The rapid advancement and widespread adoption of diffusion models highlight the urgent need for more robust theoretical underpinnings to expand their applicability to complex real-world data distributions.
This theoretical breakthrough expands the generalizability of diffusion models, making them more effective for a wider range of real-world data and applications beyond current limitations.
The prior limitations of diffusion models, based on restrictive assumptions like Lipschitz continuity or smooth manifolds, are now potentially bypassed by a universal approximation theorem.
- · AI researchers
- · Generative AI companies
- · Computer Vision developers
- · Data scientists working with complex datasets
- · AI models reliant on overly simplified data assumptions
Diffusion models can now be applied more effectively to real-world data exhibiting singularities, sharp boundaries, and disjoint clusters.
This improved theoretical foundation could accelerate the development of more robust and reliable generative AI systems for various industries.
Enhanced generative capabilities might lead to new design paradigms, accelerated scientific discovery, and more realistic synthetic data generation.
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Read at arXiv cs.LG