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SUMMARY:On the statistical analysis of denoising diffusion models - Claudi
 a Strauch (Universität Heidelberg)
DTSTART:20250625T101500Z
DTEND:20250625T111500Z
UID:TALK232246@talks.cam.ac.uk
DESCRIPTION:Diffusion-based generative models have recently attracted sign
 ificant interest in statistics and machine learning\, yet their theoretica
 l properties remain only partially understood. We study a non-standard cla
 ss of denoising reflected diffusion models that address limitations of con
 ventional designs in unbounded domains by introducing a reflected noise pr
 ocess. For these models\, we establish minimax optimal convergence rates i
 n total variation up to polylogarithmic factors under Sobolev smoothness. 
 Our analysis is based on a refined spatio-temporal approximation of the sc
 ore function via spectral methods and a rigorous treatment of neural netwo
 rk estimation. The results yield a precise characterisation of the statist
 ical complexity of this model class and provide insight into the interplay
  between geometry\, regularity\, and learnability. Based on joint work wit
 h S&ouml\;ren Christensen\, Asbj&oslash\;rn Holk\, and Lukas Trottner.
LOCATION:Seminar Room 1\, Newton Institute
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