A0360
Title: Diffusion Schrodinger bridge with applications to score-based generative modeling
Authors: Jeremy Heng - ESSEC Business School (Singapore) [presenting]
Arnaud Doucet - University of Oxford (United Kingdom)
Valentin De Bortoli - Centre National de la Recherche Scientifique (France)
James Thorton - University of Oxford (United Kingdom)
Abstract: 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), it has been recently demonstrated 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 Schrdinger Bridge problem (SB), i.e. an entropy-regularized optimal transport problem on path spaces, yields diffusions that 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 modelling experiments. The first DSB iteration recovers the existing methodology 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.
