Deep Generative Learning via Schrödinger Bridge
arXiv:2106.10410
Abstract
We propose to learn a generative model via entropy interpolation with a Schrödinger 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 with a time-varying drift term. At the sample level, we derive our Schrödinger 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 Schrödinger 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 Schrödinger 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.
References in corpus (10)
- Auto-Encoding Variational Bayes
- Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks
- GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium
- Large Scale GAN Training for High Fidelity Natural Image Synthesis
- Density estimation using Real NVP
- Mode Regularized Generative Adversarial Networks
- Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks
- Improved Techniques for Training Score-Based Generative Models
- Denoising Diffusion Implicit Models
- Generative Learning With Euler Particle Transport