Improving Medical Image Generative Models with Fréchet Distance Loss
Authors: Andrew Marshall, Xuanang Xu, Xiaoran Zhang, Rui Wang, Lawrence Staib, James Duncan
Organizations: Department of Biomedical Engineering, Yale University · Department of Radiology & Biomedical Imaging, Yale University · Department of Electrical Engineering, Yale University
Abstract
Diffusion generative models have demonstrated immense potential for synthetic medical image generation. However, these models often struggle to capture complex morphological characteristics of heterogeneous tumors with irregular boundaries, limiting their utility for downstream clinical tasks such as segmentation. This limitation stems from the standard denoising objective: minimizing a per-pixel error, which smooths high-variance irregular structures characteristic of tumors. To address this, we propose finetuning these generative models with Fréchet Distance loss (FD-loss). FD-loss aligns the first and second order feature statistics of real and generated images in a pretrained encoder space, encouraging the generator to capture complex structural variations characteristic of heterogeneous tumors. We integrate FD-loss across diverse architectural settings, using both natural- and medical-image encoders on multiple liver and brain cancer datasets spanning CT and MRI modalities. Downstream segmentation networks trained on our FD-regularized synthetic data consistently achieve superior performance, improving tumor DSC by >$$5\% over unregularized synthetic augmentation alone. Qualitative analysis suggests these gains are associated with more faithful tumor synthesis and fewer segmentation hallucinations. Our results show FD-loss as an effective regularizer for medical image generative models to improve clinical workflows.
Fréchet distance has recently emerged as an effective distribution-level objective for generator post-training, complementing the conventional sample-level diffusion and flow-matching losses. However, directly optimizing Fréchet objectives can cause Fréchet hacking. The target metrics keep improving, but visual quality and Fréchet alignment in other feature spaces may stagnate or deteriorate. We attribute this failure to the static pretrained feature spaces used by existing Fréchet losses. These feature spaces provide incomplete and fixed views of the differences between real and generated distributions. To address this limitation, we propose Adversarial Fréchet Distance (AdvFD), which complements the static representation targets in FD-Loss with a calibrated adversarially learned representation. AdvFD augments the original static Fréchet objective with a learnable representation that adversarially maximizes the Fréchet discrepancy between real and generated samples, while the generator minimizes the same discrepancy in the resulting adaptive feature space. To prevent the adversarial representation from trivially increasing the objective through feature amplification, we further introduce real-feature whitening, which normalizes its scale and covariance geometry and stabilizes the min--max optimization. Extensive experiments show that AdvFD consistently improves one-step generator post-training across both JiT and pMF backbones and across different model scales.
Diffusion models produce high-quality synthetic data but suffer from slow inference. We propose 3D Variable-Step Denoising Diffusion Probabilistic Model (VS-DDPM) a framework engineered to maintain generative quality while accelerating inference by several factors. We tested our approach on four tasks (missing MRI, tumor removal, MRI-to-sCT, and CBCT-to-sCT) within the BraTS2025 and SynthRAD2025 challenges. Designed for high efficiency under hardware and time constrains imposed by both challenges. VS-DDPM achieved state-of-the-art (SOTA) performance in missing MRI synthesis, yielding Dice scores of 0.80, 0.83, and 0.88 for the enhancing tumor, tumor core, and whole tumor regions, respectively, alongside a structural similarity index (SSIM) of 0.95. For MRI tumor removal, the model attained a root mean squared error (RMSE) of 0.053, a peak signal-to-noise ratio (PSNR) of 26.77, and an SSIM of 0.918. While the framework demonstrated competitive performance in MRI-to-sCT and CBCT-to-sCT tasks, it did not reach SOTA benchmarks, potentially due to sensitivities in data pre and post-processing pipelines or specific loss function configurations. These results demonstrate that VS-DDPM provides a robust and tunable solution for high-fidelity 3D medical image synthesis. The code is available in https://github.com/andre-fs-ferreira/SynthRAD_by_Faking_it.
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 achieves0.72 FID on ImageNet 256x256. 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 FDrk, 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.