Machine Learning Seminar: Pieper-Sethmacher -- Infinite-dimensional generative diffusions via Doob's h-transform

The details about the machine learning seminar are as follows: 

Time: Mon 12 Oct (2:00 - 3:00pm): 

Location: SMRI Seminar Room (A12-03-301) A12 Macleay Building, Level 3, Room 301.  

Speaker: Thorben Pieper-Sethmacher (USYD) 

Title: Infinite-dimensional generative diffusions via Doob's h-transform 

Abstract: Diffusion models are one of the stables of modern generative machine
learning.  Recently, there has been an increasing interest in their extension from the
finite-dimensional to the infinite-dimensional function space setting.  In this talk, we
will revisit diffusion models, the challenges one encounters during this extension and
the current state of the literature on how to overcome these challenges.  We then
present recent results that formulate a generative diffusion model based on Doob's
h-transform.  Rather than relying on time reversal of a noising process, a reference
diffusion is forced towards the target distribution by an exponential change of
measure.  Compared to existing methodology, this approach readily generalises to the
infinite-dimensional setting, hence offering greater flexibility in the diffusion
model.  The construction is derived rigorously under verifiable conditions, and bounds
with respect to the target measure are established.