تقرير
On the Asymptotic Mean Square Error Optimality of Diffusion Models
| العنوان: | On the Asymptotic Mean Square Error Optimality of Diffusion Models |
|---|---|
| المؤلفون: | Fesl, Benedikt, Böck, Benedikt, Strasser, Florian, Baur, Michael, Joham, Michael, Utschick, Wolfgang |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Statistics |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Statistics - Machine Learning |
| الوصف: | Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy inspired by the structure of the MSE-optimal conditional mean estimator (CME). The resulting DM-based denoiser can be conveniently employed using a pre-trained DM, being particularly fast by truncating reverse diffusion steps and not requiring stochastic re-sampling. We present a comprehensive (non-)asymptotic optimality analysis of the proposed diffusion-based denoiser, demonstrating polynomial-time convergence to the CME under mild conditions. Our analysis also derives a novel Lipschitz constant that depends solely on the DM's hyperparameters. Further, we offer a new perspective on DMs, showing that they inherently combine an asymptotically optimal denoiser with a powerful generator, modifiable by switching re-sampling in the reverse process on or off. The theoretical findings are thoroughly validated with experiments based on various benchmark datasets. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.02957 |
| رقم الأكسشن: | edsarx.2403.02957 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |