REFINING DEEP GENERATIVE MODELS VIA DISCRIMINATOR GRADIENT FLOW

Abstract

Deep generative modeling has seen impressive advances in recent years, to the point where it is now commonplace to see simulated samples (e.g., images) that closely resemble real-world data. However, generation quality is generally inconsistent for any given model and can vary dramatically between samples. We introduce Discriminator Gradient f low (DGf low), a new technique that improves generated samples via the gradient flow of entropy-regularized f -divergences between the real and the generated data distributions. The gradient flow takes the form of a non-linear Fokker-Plank equation, which can be easily simulated by sampling from the equivalent McKean-Vlasov process. By refining inferior samples, our technique avoids wasteful sample rejection used by previous methods (DRS & MH-GAN). Compared to existing works that focus on specific GAN variants, we show our refinement approach can be applied to GANs with vector-valued critics and even other deep generative models such as VAEs and Normalizing Flows. Empirical results on multiple synthetic, image, and text datasets demonstrate that DGf low leads to significant improvement in the quality of generated samples for a variety of generative models, outperforming the state-of-the-art Discriminator Optimal Transport (DOT) and Discriminator Driven Latent Sampling (DDLS) methods.

1. INTRODUCTION

Deep generative models (DGMs) have excelled at numerous tasks, from generating realistic images (Brock et al., 2019) to learning policies in reinforcement learning (Ho & Ermon, 2016) . Among the variety of proposed DGMs, Generative Adversarial Networks (GANs) (Goodfellow et al., 2014) have received widespread popularity for their ability to generate high quality samples that resemble real data. Unlike Variational Autoencoders (VAEs) (Kingma & Welling, 2014) and Normalizing Flows (Rezende & Mohamed, 2015; Kingma & Dhariwal, 2018) , GANs are likelihood-free methods; training is formulated as a minimax optimization problem involving a generator and a discriminator. The generator seeks to generate samples that are similar to the real data by minimizing a measure of discrepancy (between the generated samples and real samples) furnished by the discriminator. The discriminator is trained to distinguish the generated samples from the real samples. Once trained, the generator is used to simulate samples and the discriminator has traditionally been discarded. However, recent work has shown that discarding the discriminator is wasteful -it actually contains useful information about the underlying data distribution. This insight has led to sample improvement techniques that use this information to improve the quality of generated samples (Azadi et al., 2019; Turner et al., 2019; Tanaka, 2019; Che et al., 2020) . Unfortunately, current methods either rely on wasteful rejection operations in the data space (Azadi et al., 2019; Turner et al., 2019) , or require a sensitive diffusion term to ensure sample diversity (Che et al., 2020) . Prior work has also focused on improving GANs with scalar-valued discriminators, which excludes a large family of GANs with vector-valued critics, e.g., MMDGAN (Li et al., 2017; Bińkowski et al., 2018) and OCFGAN (Ansari et al., 2020) , and likelihood-based generative models.

