arXiv:2602.02908v2 Announce Type: replace-cross Abstract: Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across splits already predict much of the generated images. To formalize this, we develop a random matrix theory (RMT) framework that quantifies how finite datasets shape the expectation and variance of the learned denoiser and sampling map in the linear setting. For expectations, sampling variability acts a
This research provides a theoretical framework to understand the surprising consistency observed in diffusion models, a leading AI generation technique, which has significant implications for their reliability and training methods.
Understanding the fundamental mathematical properties of diffusion models allows for more robust development, better performance prediction, and potentially more efficient training, impacting the broader AI ecosystem.
The theoretical understanding of diffusion model consistency, previously an empirical observation, now has a formal mathematical basis, which could lead to novel architectural designs or training strategies.
- · AI Researchers
- · Deep Learning Framework Developers
- · Companies utilizing diffusion models for content generation
- · AI models without strong theoretical underpinnings
This theoretical advance could lead to more stable and predictable generative AI models.
Improved model stability might reduce the computational resources needed for training, impacting the compute supply chain.
More reliable generated content could accelerate the adoption of AI agents in various creative and industrial applications.
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Read at arXiv cs.AI