Generative models can be categorized into two types: explicit generative models that define explicit density forms and allow exact likelihood inference, such as score-based diffusion models (SDMs) and normalizing flows; implicit generative models that directly learn a transformation from the prior to the data distribution, such as generative adversarial nets (GANs). While these two types of models have shown great success, they suffer from respective limitations that hinder them from achieving fast sampling and high sample quality simultaneously. In this paper, we propose a unified theoretic framework for SDMs and GANs. We shown that: i) the learning dynamics of both SDMs and GANs can be described as a novel SDE named Discriminator Denoising Diffusion Flow (DiffFlow) where the drift can be determined by some weighted combinations of scores of the real data and the generated data; ii) By adjusting the relative weights between different score terms, we can obtain a smooth transition between SDMs and GANs while the marginal distribution of the SDE remains invariant to the change of the weights; iii) we prove the asymptotic optimality and maximal likelihood training scheme of the DiffFlow dynamics; iv) under our unified theoretic framework, we introduce several instantiations of the DiffFLow that provide new algorithms beyond GANs and SDMs with exact likelihood inference and have potential to achieve flexible trade-off between high sample quality and fast sampling speed.

翻译：生成模型可分为两类：一类是定义显式密度形式并允许精确似然推断的显式生成模型，例如基于分数的扩散模型和归一化流；另一类是直接学习从先验分布到数据分布变换的隐式生成模型，例如生成对抗网络。尽管这两类模型取得了巨大成功，但各自存在局限性，阻碍其同时实现快速采样和高样本质量。本文针对SDMs与GANs提出统一的理论框架，证明：(i) SDMs与GANs的学习动力学均可描述为一种名为判别器去噪扩散流的新型随机微分方程，其漂移项由真实数据与生成数据的分数加权组合决定；(ii) 通过调整不同分数项的相对权重，可在SDMs与GANs之间实现平滑过渡，同时保持SDE边际分布对权重变化不变；(iii) 证明了DiffFlow动力学的渐近最优性与极大似然训练机制；(iv) 在该统一理论框架下，引入DiffFlow的若干实例化方法，这些方法提供了超越GANs与SDMs的新算法，支持精确似然推断，并有望实现高样本质量与快速采样速度的灵活权衡。