Representation Fréchet Loss for Visual Generation

We show that Fréchet Distance (FD), long considered impractical as a training objective, can in fact be effectively optimized in the representation space. Our idea is simple: decouple the population size for FD estimation (e.g., 50k) from the batch size for gradient computation (e.g., 1024). We term this approach FD-Loss. Optimizing FD-Loss reveals several surprising findings. First, post-training a base generator with FD-Loss in different representation spaces consistently improves visual quality. Under the Inception feature space, a one-step generator achieves 0.72 FID on ImageNet $256\times256$. Second, the same FD-Loss repurposes multi-step generators into strong one-step generators without teacher distillation, adversarial training or per-sample targets. Third, FID can misrank visual quality: modern representations can yield better samples despite worse Inception FID. This motivates FDr$^{k}$, a multi-representation metric. We hope this work will encourage further exploration of distributional distances in diverse representation spaces as both training objectives and evaluation metrics for generative models. Code and checkpoints will be open-sourced.