We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for $N$ dimensional data by embedding paths in $N{+}D$ dimensional space while still controlling the progression with a simple scalar norm of the $D$ additional variables. The new models reduce to PFGM when $D{=}1$ and to diffusion models when $D{\to}\infty$. The flexibility of choosing $D$ allows us to trade off robustness against rigidity as increasing $D$ results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of $D$, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models ($D{\to} \infty$) to any finite $D$ values. Our experiments show that models with finite $D$ can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ $64{\times}64$ datasets, with FID scores of $1.91/2.43$ when $D{=}2048/128$. In class-conditional setting, $D{=}2048$ yields current state-of-the-art FID of $1.74$ on CIFAR-10. In addition, we demonstrate that models with smaller $D$ exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

翻译：我们提出了一类新的物理启发式生成模型，称为PFGM++，它统一了扩散模型和泊松流生成模型（PFGM）。这些模型通过在$N{+}D$维空间中嵌入路径，同时仍用$D$个附加变量的简单标量范数控制进程，来实现$N$维数据的生成轨迹。当$D{=}1$时，新模型退化为PFGM；当$D{\to}\infty$时，退化为扩散模型。选择$D$的灵活性使我们能够权衡鲁棒性与刚性——随着$D$增加，数据与附加变量范数之间的耦合更加集中。我们摒弃了PFGM中有偏的大批量场目标，转而提供类似于扩散模型的无偏扰动目标。为探索不同的$D$值，我们提供了一种直接对齐方法，可将扩散模型（$D{\to}\infty$）中经过良好调优的超参数迁移至任意有限$D$值。实验表明，有限$D$值的模型在CIFAR-10/FFHQ $64{\times}64$数据集上可超越先前最优的扩散模型：当$D{=}2048/128$时，FID分数分别为$1.91/2.43$。在类别条件设置下，$D{=}2048$在CIFAR-10上取得了当前最优FID值$1.74$。此外，我们证明了较小$D$值的模型对建模误差表现出更强的鲁棒性。代码见 https://github.com/Newbeeer/pfgmpp