Task (in ML perspective)
Image generation
Related works
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To learn a nonlinear function to transform a simple reference dist. to the target dist. as a data generating mechanisms
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Likelihood-based model
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e.g.) VAE
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- Consistency results require that the data dist. is within the model family, which is often hard to hold in practive
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Implicit generative model
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e.g.) GAN
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Evolving time to go to infinity at the population level
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e.g.) flow-based model, Stochastic differential equations
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- Needs strong assumption to achieve model consistency: the target must be long-concave or satisfy the log-Sovolev inequality
Goal
To generate high-quality image
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with consistency based on mild assumption
Consistency?
Problem definition
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Schrödinger Bridge tackles the problem by interpolating a reference distribution to a target distribution based on the Kullback-Leibler divergence.
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Formulated via an SDE on a finite time interval [0, 1] with a time-varying drift term at the population level
Jargons
-field (i.e. -algebra)
Methods
Two- stage Schro ̈dinger Bridge algorithm
by plugging the drift term estimated by a deep score estimator and a deep density estimator in the Euler-Maruyama method
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Dataset: CIFAR-10, Celeb A
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Method
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input : Observed data points
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output : Data dist.
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Generative process: Extract data point from learned data dist.
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Detailed method
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Background
Problem formulation of Schröndinger bridge (SBP)
[Proposed method]: two-stage approach
Consistency 증명
Results
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Image interpolation
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Image inpainting
