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UID:20240226T1327Z-1708954025.7807-EO-30743-4@10.1.1.165
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SUMMARY: Jeremy Heng (ESSEC Business School) – Diffusion Schrödinger Bridge
with Applications to Score-Based Generative Modeling
DESCRIPTION: Progressively applying Gaussian noise transforms complex data
distributions to approximately Gaussian. Reversing this dynamic defines a g
enerative model. When the forward noising process is given by a Stochastic
Differential Equation (SDE)\, Song et al. (2021) demonstrate how the time i
nhomogeneous drift of the associated reverse-time SDE may be estimated usin
g score-matching. A limitation of this approach is that the forward-time SD
E must be run for a sufficiently long time for the final distribution to be
approximately Gaussian.
X-ALT-DESC;FMTTYPE=text/html: #### Diffusion Schrödinger Bridge with Applica
tions to Score-Based Generative Modeling

February 29\, 2024 10:00 AM
Singapore (**Registration
starts at 09:50 AM**)

#### Abstract

Progressively a
pplying Gaussian noise transforms complex data distributions to approximate
ly Gaussian. Reversing this dynamic defines a generative model. When the fo
rward noising process is given by a Stochastic Differential Equation (SDE)\
, Song et al. (2021) demonstrate how the time inhomogeneous drift of the as
sociated reverse-time SDE may be estimated using score-matching. A limitati
on of this approach is that the forward-time SDE must be run for a sufficie
ntly long time for the final distribution to be approximately Gaussian. In
contrast\, solving the Schrödinger Bridge problem (SB)\, i.e. an entropy-re
gularized optimal transport problem on path spaces\, yields diffusions whic
h generate samples from the data distribution in finite time. We present Di
ffusion SB (DSB)\, an original approximation of the Iterative Proportional
Fitting (IPF) procedure to solve the SB problem\, and provide theoretical a
nalysis along with generative modeling experiments. The first DSB iteration
recovers the methodology proposed by Song et al. (2021)\, with the flexibi
lity of using shorter time intervals\, as subsequent DSB iterations reduce
the discrepancy between the final-time marginal of the forward (resp. backw
ard) SDE with respect to the prior (resp. data) distribution. Beyond genera
tive modeling\, DSB offers a widely applicable computational optimal transp
ort tool as the continuous state-space analogue of the popular Sinkhorn alg
orithm (Cuturi\, 2013).

**Papers:**

https://arxiv.o
rg/abs/2106.01357

#### About the Speaker

Jeremy Heng completed
his DPhil in Statistics at the University of Oxford in 2016. He was a post
doctoral fellow in the Department of Statistics at Harvard University from
2016 to 2018\, before joining ESSEC Business School on the Singapore campus
as an Assistant Professor of Statistics in 2019. His research interests co
ver various areas of computational statistics\, optimal transport and optim
al control.

*For more information about the ESD Seminar\, ple
ase email esd_invite@sutd.edu.sg*

CATEGORIES:ESD Research Seminar Series,Special Seminars
LOCATION:Data Analytics Lab (Building 1\, Level 6\, Room 1.610)
GEO:0.000000;0.000000
ORGANIZER;CN="SUTDPillarAdministrator":MAILTO:websupport@sutd.edu.sg
URL;VALUE=URI:https://esd.sutd.edu.sg/news-events/research-seminar-series/j
eremy-heng-essec-business-school-diffusion-schrodinger-bridge-with-applicat
ions-to-score-based-generative-modeling/
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DTSTART:20230301T020000
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