FD-Loss

Representation Fréchet Loss for Visual Generation

Jiawei Yang, Zhengyang Geng, Xuan Ju, Yonglong Tian, Yue Wang · arXiv 2026

Read paper · arXiv:2604.28190

Estimate a larger feature population from historical statistics while backpropagating Fréchet distance through the current batch only.

What you will implement

EMA of raw first and second moments, covariance recovery, differentiable Fréchet distance, and multi-representation loss normalization.

• 52. FD-loss Population Moments and EMA

  Track population information through raw first and second moments while differentiating only the current microbatch.

  Implement the default EMA statistics estimator with a supplied deterministic feature stream. FIFO queues, multiple GPUs, image feature extraction and a generator are outside this module.

• 53. FD-loss Differentiable Fréchet Objective

  Differentiate Gaussian population Fréchet distance and normalize representation losses with a stopped denominator.

  Implement Eq. (2), Eq. (6), and the symmetric trace algorithm from Appendix B.3. EMA, the 2D generator and the optimizer loop are provided; no image representation model is trained.