Oberseminar Wissenschaftliches Rechnen (Emanuel Pfarr)

Generative diffusion models have emerged as a leading approach in modern generative modeling.
These models rely on a stochastic process that bridges an unknown data distribution with a wellunderstood
reference distribution. Despite their empirical success, current diffusion models are
subject to several sources of error. These include approximation errors arising from the use of neural
networks to estimate intractable quantities, discretization errors introduced when simulating
continuous-time processes, and truncation errors due to terminating the process at a finite time.
By integrating tools from numerical analysis and stochastic process theory, a rigorous mathematical
understanding of diffusion models can be developed, enabling a systematic characterization
and mitigation of these sources of error.