论文标题
通过最佳传输了解DDPM潜在代码
Understanding DDPM Latent Codes Through Optimal Transport
论文作者
论文摘要
扩散模型最近超出了替代方法，用于建模自然图像的分布，例如gan。这样的扩散模型允许通过概率流ode进行确定性采样，从而产生潜在空间和编码器映射。尽管具有重要的实际应用，例如对可能性的估计，但该地图的理论特性尚未完全理解。在目前的工作中，我们针对VP SDE（DDPM）方法的流行情况部分解决了这个问题。我们表明，也许令人惊讶的是，DDPM编码器映射与公共分布的最佳传输图相吻合。我们在理论上和广泛的数值实验上支持这一主张。
Diffusion models have recently outperformed alternative approaches to model the distribution of natural images, such as GANs. Such diffusion models allow for deterministic sampling via the probability flow ODE, giving rise to a latent space and an encoder map. While having important practical applications, such as estimation of the likelihood, the theoretical properties of this map are not yet fully understood. In the present work, we partially address this question for the popular case of the VP SDE (DDPM) approach. We show that, perhaps surprisingly, the DDPM encoder map coincides with the optimal transport map for common distributions; we support this claim theoretically and by extensive numerical experiments.
