  Particle-based deep generative models, such as gradient flows and score-based
diffusion models, have recently gained traction thanks to their striking
performance. Their principle of displacing particle distributions using
differential equations is conventionally seen as opposed to the previously
widespread generative adversarial networks (GANs), which involve training a
pushforward generator network. In this paper we challenge this interpretation,
and propose a novel framework that unifies particle and adversarial generative
models by framing generator training as a generalization of particle models.
This suggests that a generator is an optional addition to any such generative
model. Consequently, integrating a generator into a score-based diffusion model
and training a GAN without a generator naturally emerge from our framework. We
empirically test the viability of these original models as proofs of concepts
of potential applications of our framework.
