Deep Generative Learning via Schrödinger Bridge

By Gefei Wang, Yuling Jiao, Qiang Xu, Yang Wang, Can Yang. 2021

148 citations recorded by the source corpus.

We propose to learn a generative model via entropy interpolation with a Schr\"{o}dinger Bridge. The generative learning task can be formulated as interpolating between a reference distribution and a target distribution based on the Kullback-Leibler divergence. At the population level, this entropy interpolation is characterized via an SDE on $[0,1]$ with a time-varying drift term. At the sample level, we derive our Schr\"{o}dinger Bridge algorithm by plugging the drift term estimated by a deep score estimator and a deep density ratio estimator into the Euler-Maruyama method. Under some mild smoothness assumptions of the target distribution, we prove the consistency of both the score estimator and the density ratio estimator, and then establish the consistency of the proposed Schr\"{o}dinger Bridge approach. Our theoretical results guarantee that the distribution learned by our approach converges to the target distribution. Experimental results on multimodal synthetic data and benchmark data support our theoretical findings and indicate that the generative model via Schr\"{o}dinger Bridge is comparable with state-of-the-art GANs, suggesting a new formulation of generative learning. We demonstrate its usefulness in image interpolation and image inpainting.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

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Citations in the corpus

Flow Matching for Generative Modeling (2022, background): “In an another line of works, (De Bortoli et al., 2021; Wang et al., 2021; Peluchetti, 2021) proposed finite time diffusion constructions via diffusion bridges theory resolving the approximation error incurred by infinite time denoising constructions.”
Non-Denoising Forward-Time Diffusions (2023, methodology): “We remark the simplicity of the proposed DBMT approach (Algorithms 1 and 2) compared to alternatives grounded in the Schrödinger bridge problem (De Bortoli et al., 2021; Wang et al., 2021; Vargas et al., 2021).”
Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling (2021, methodology): “It also differs from (Finlay et al., 2020) which approximates the SB solution by a diffusion whose drift is computed using potentials of the dual formulation of SB. Finally, Wang et al. (2021) have recently proposed to perform generative modeling by solving not one but two SB problems.”
Fast Sampling of Diffusion Models with Exponential Integrator (2022, background): “Another strategy to make the forward diffusion nonlinear and trainable (Zhang & Chen, 2021; Vargas et al., 2021; De Bortoli et al., 2021; Wang et al., 2021; Chen et al., 2021a) in the spirit of Schr¨odinger bridge (Chen et al., 2021b).”
Improving and generalizing flow-based generative models with minibatch optimal transport (2023, unknown): “%) computational overhead during training.”
Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow (2022, background): “Another body of works [87, 11, 7, 82] leverages Schrodinger bridges (SB) as an alternative approach to learning diffusion generative models.”