Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling

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


Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE), Song et al. (2021) demonstrate how the time inhomogeneous drift of the associated reverse-time SDE may be estimated using score-matching. A limitation of this approach is that the forward-time SDE must be run for a sufficiently long time for the final distribution to be approximately Gaussian. In contrast, solving the Schrödinger Bridge problem (SB), i.e. an entropy-regularized optimal transport problem on path spaces, yields diffusions which generate samples from the data distribution in finite time. We present Diffusion SB (DSB), an original approximation of the Iterative Proportional Fitting (IPF) procedure to solve the SB problem, and provide theoretical analysis along with generative modeling experiments. The first DSB iteration recovers the methodology proposed by Song et al. (2021), with the flexibility of using shorter time intervals, as subsequent DSB iterations reduce the discrepancy between the final-time marginal of the forward (resp. backward) SDE with respect to the prior (resp. data) distribution. Beyond generative modeling, DSB offers a widely applicable computational optimal transport tool as the continuous state-space analogue of the popular Sinkhorn algorithm (Cuturi, 2013).



About the Speaker

Jeremy Heng completed his DPhil in Statistics at the University of Oxford in 2016. He was a postdoctoral 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 cover various areas of computational statistics, optimal transport and optimal control.

Jeremy Heng (ESSEC Business School) - Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling

For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg