Toward Physical Generative Models

Explore the mathematical foundations of generative models through a dynamical systems lens in this hour-long lecture by Nisha Chandramoorthy from the University of Chicago. Examine score-based diffusions and flow-matching-type generative models as random dynamical systems to understand their fundamental properties and effectiveness. Investigate whether generative models produce "physical" samples that remain close to the support of true target distributions despite algorithmic errors. Delve into the concept of lazy generative models, where random dynamical systems are applied to target samples to create distributions approaching Gaussian form at finite times. Analyze the conditions under which the noising process can be approximately inverted to recover samples from similar support regions. Learn about cutting-edge research combining probability theory, dynamical systems, and machine learning, with insights from collaborative work with researchers from the University of Chicago and University of Sydney.