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

DiffFlow: A Unified SDE Framework for Score-Based Diffusion Models and Generative Adversarial Networks