Score-based generative models have demonstrated state-of-the-art performance in numerous applications in recent years. The central concept behind these models involves the gradual injection of noise into the training data, followed by learning the reverse process to generate new samples. The training and sampling procedures can be conducted independently. The learning phase is facilitated by noise-conditional score networks, while sampling can be accomplished through various methods, including Langevin Monte Carlo approaches, stochastic differential equations, ordinary differential equations, and various combinations.

In this seminar, we will begin by reviewing generative models and examining the most common architectures used in current research. Special attention will be given to comparing different objective functions needed for training, as well as the different sampling procedures. We will explore invertible neural networks, with a particular focus on normalizing flows and continuous normalizing flows. Subsequently, we will address score matching and Langevin dynamics for score-based generative models. This includes an explanation of how Langevin dynamics can be used to approximate scores, deriving noise-conditional score networks, and providing a detailed explanation of the training process. Additionally, we will explore a broader generalization involving an infinite number of time steps for noise levels, studying the process using stochastic differential equations. This formulation, known as score SDEs, leverages SDEs for noise perturbation and sample generation. The seminar will conclude with a comparison to other possible diffusion models and a discussion of further enhancements in sample generation.

The seminar is scheduled for the second half of the winter term.

• Prerequisites: Basic knowledge in probability theory and statistics
• Registration: Via email to Jonathan
• First (organizational) meeting: Friday, 26 April at 14:00 c.t.
• Time and Location: Friday 14:00 c.t. (The location will be announced soon)

Further information on the seminar will be announced in the first organizational meeting. For any specific question you can contact Jonathan Schwarz.

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